Samacheer Kalvi solutions for Mathematics [English] Class 8 TN Board chapter 1 - Numbers [Latest edition]

`(-19)/5` lies between the integers __________ and __________

The decimal form of the rational number `15/(-4)` is __________

The rational numbers `(-8)/3` and `8/3` are equidistant from __________

The next rational number in the sequence `(-15)/24, 20/(-32), (-25)/40` is __________

The standard form of `58/(-78)` is __________

0 is the smallest rational number

`(-4)/5` lies to the left of `(-3)/4`

`(-19)/5` is greater than `15/(-4)`

The average of two rational numbers lies between them

There are an unlimited number of rational numbers between 10 and 11

Find the rational numbers represented by the question marks marked on the following number line

Find the rational numbers represented by the question marks marked on the following number line

Find the rational numbers represented by the question marks marked on the following number line

The points S, Y, N, C, R, A, T, I and O on the number line are such that CN = NY = YS and RA = AT = TI = IO. Find the rational numbers represented by the letters Y, N, A, T and I

Draw a number line and represent the following rational numbers on it

`9/4`

Draw a number line and represent the following rational numbers on it

`(-8)/3`

Draw a number line and represent the following rational numbers on it

`(-17)/(-5)`

Draw a number line and represent the following rational numbers on it

`15/(-4)`

Write the decimal form of the following rational numbers

`1/11`

Write the decimal form of the following rational numbers

`13/4`

Write the decimal form of the following rational numbers

`(-18)/7`

Write the decimal form of the following rational numbers

`1 2/5`

Write the decimal form of the following rational numbers

`-3 1/2`

List any five rational numbers between the given rational numbers

−2 and 0

List any five rational numbers between the given rational numbers

`(-1)/2` and `3/5`

List any five rational numbers between the given rational numbers

`1/4` and `7/20`

List any five rational numbers between the given rational numbers

`(-6)/4` and `(-23)/10`

Use the method of average to write 2 rational numbers between `14/5` and `16/3`

Compare the following pair of rational numbers

`(-11)/5, (-21)/8`

Compare the following pair of rational numbers

`3/(-4), (-1)/2`

Compare the following pair of rational numbers

`2/3, 4/5`

Arrange the following rational numbers in ascending and descending order

`(-5)/12, (-11)/8, (-15)/24, (-7)/(-9), 12/36`

Arrange the following rational numbers in ascending and descending order

`(-17)/10, (-7)/5, 0, (-2)/4, (-19)/20`

The number which is subtracted from `(-6)/11` to get `8/9` is __________

Which of the following pairs is equivalent?

`(-5)/4` is a rational number which lies between __________

Which of the following rational numbers is the greatest?

The sum of the digits of the denominator in the simplest form of `112/528` is _________

The value of `(-5)/12 + 7/15` = ________

The value of `((-3)/6) xx (18/(-9))` is ________

The value of `((-15)/23) ÷ (30/(-46))` is ________

The rational number ________ does not have a reciprocal

The multiplicative inverse of –1 is ________

All rational numbers have an additive inverse

The rational numbers that are equal to their additive inverses are 0 and –1

The additive inverse of `(-11)/(-17)` is `11/17`

The rational number which is its own reciprocal is –1

The multiplicative inverse exists for all rational numbers

Find the sum: `7/5 + 3/5`

Find the sum: `7/5 + 5/7`

Find the sum: `6/5 + ((-14)/15)`

Find the sum: `-4 2/3 + 7 5/12`

Subtract : `(-8)/44` from `(-17)/11` 

Evaluate : `9/132 xx (-11)/3`

Evaluate : `(-7)/27 xx 24/(-35)`

Divide : `(-21)/5` by `(-7)/(-10)` 

Divide : `(-3)/13` by −3

Divide : −2 by `(-6)/(15)`

Find (a + b) ÷ (a – b) if a = `1/2`, b = `2/3`

Find (a + b) ÷ (a – b) if a = `(-3)/5`, b = `2/15`

Simplify : `1/2 + (3/2 - 2/5) ÷ 3/10 xx 3` and show that it is a rational number between 11 and 12

Simplify : `[11/8 xx ((-6)/33)] + [1/3 + (3/5 ÷ 9/20)] - [4/7 xx (-7)/5]`

Simplify : `[4/3 ÷ (8/(-7))] - [3/4 xx 4/3] + [4/3 xx ((-1)/4)]`

A student had multiplied a number by `4/3` instead of dividing it by `4/3` and got 70 more than the correct answer. Find the number

The standard form of the sum `3/4 + 5/6 + ((-7)/12)` is __________

`(3/4 - 5/8) + 1/2` = __________

`3/4 ÷ (5/8 + 1/2)` = __________

`3/4 xx (5/8 ÷ 1/2)` = __________

Which of these rational numbers which have additive inverse?

Verify the closure property for addition and multiplication for the rational numbers `(-5)/7` and `8/9`

Verify the commutative property for addition and multiplication for the rational numbers `(-10)/11` and `(-8)/33`

Verify the associative property for addition and multiplication for the rational number `(-7)/9, 5/6` and `(-4)/3`

Verify the distributive property a × (b + c) = (a × b) + (a + c) for the rational numbers a = `(-1)/2`, b = `2/3` and c = `(-5)/6`

Verify the identity property for addition and multiplication for the rational numbers `15/19` and `(-18)/25`

Verify the additive and multiplicative inverse property for the rational numbers `(-7)/17` and `17/27`

Closure property is not true for division of rational numbers because of the number

`1/2 - (3/4 - 5/6) ≠ (1/2 - 3/4) - 5/6` illustrates that subtraction does not satisfy the ________ property for rational numbers

Which of the following illustrates the inverse property for addition?

`3/4 xx (1/2 - 1/4) = 3/4 xx 1/2 - 3/4 xx 1/4` illustrates that multiplication is distributive over

The ones digit in the square of 77 is ___________

The number of non-square numbers between 24² and 25² is ______

The number of perfect square numbers between 300 and 500 is ______

If a number has 5 or 6 digits in it, then its square root will have ___________ digits

The value of `sqrt(180)` lies between integers ______ and ______

When a square number ends in 6, its square root will have 6 in the unit’s place

A square number will not have odd number of zeros at the end

The number of zeros in the square of 91000 is 9

The square of 75 is 4925

The square root of 225 is 15

Find the square of the following number

17

Find the square of the following number

203

Find the square of the following number

1098

Examine if the following is a perfect square

725

Examine if the following is a perfect square

190

Examine if the following is a perfect square

841

Examine if the following is a perfect square

1089

Find the square root by prime factorisation method

144

Find the square root by prime factorisation method

256

Find the square root by prime factorisation method

784

Find the square root by prime factorisation method

1156

Find the square root by prime factorisation method

4761

Find the square root by prime factorisation method

9025

Find the square root by long division method

1764

Find the square root by long division method

6889

Find the square root by long division method

11025

Find the square root by long division method

17956

Find the square root by long division method

418609

Estimate the value of the following square root to the nearest whole number:

`sqrt(440)`

Estimate the value of the following square root to the nearest whole number:

`sqrt(800)`

Estimate the value of the following square root to the nearest whole number:

`sqrt(1020)`

Find the square root of the following decimal numbers and fractions

2.89

Find the square root of the following decimal numbers and fractions

67.24

Find the square root of the following decimal numbers and fractions

2.0164

Find the square root of the following decimal numbers and fractions

`144/225`

Find the square root of the following decimal numbers and fractions

`7 18/49`

Find the least number that must be subtracted to 6666 so that it becomes a perfect square. Also, find the square root of the perfect square thus obtained

Find the least number by which 1800 should be multiplied so that it becomes a perfect square. Also, find the square root of the perfect square thus obtained

The square of 43 ends with the digit ______

_______ is added to 24² to get 25² 

`sqrt(48)` is approximately equal to ______

`sqrt(128) - sqrt(98) + sqrt(18)` = ______

The number of digits in the square root of 123454321 is ______ 

The ones digits in the cube of 73 is ____________

The maximum number of digits in the cube of a two digit number is _______

The smallest number to be added to 3333 to make it a perfect cube is ___________

The cube root of 540 × 50 is ___________

The cube root of 0.000004913 is ___________

The cube of 24 ends with the digit 4

Subtracting 10³ from 1729 gives 9³ 

The cube of 0.0012 is 0.000001728

79570 is not a perfect cube

The cube root of 250047 is 63

Show that 1944 is not a perfect cube

Find the smallest number by which 10985 should be divided so that the quotient is a perfect cube

Find the smallest number by which 200 should be multiplied to make it a perfect cube

Find the cube root 24 × 36 × 80 × 25

Find the cube root of 729 and 6859 prime factorisation

What is the square root of cube root of 46656?

If the cube of a squared number is 729, find the square root of that number

Find two smallest perfect square numbers which when multiplied together gives a perfect cube number

`(-1)^("even integer")` is _____________

For a ≠ 0, a⁰ is ______________

4⁻³ × 5⁻³ = __________

(−2)⁻⁷ = ____________

`(-1/3)^(-5)` = ____________

If 8^x = `1/64`, the value of x is −2

The simplified form of `(256)^((-1)/4) xx 4^2` is `1/4`

Using the power rule, (3⁷)⁻² = 3⁵

The standard form of 2 × 10⁻⁴ is 0.0002

The scientific form of 123.456 is 1.23456 × 10⁻² 

Evaluate: `(1/2)^3`

Evaluate: `(1/2)^(-5)`

Evaluate: `((-5)/6)^(-3)`

Evaluate: (2⁻⁵ × 2⁷) ÷ 2⁻² 

Evaluate: (2⁻¹ × 3⁻¹) ÷ 6⁻² 

Evaluate: `(2/5)^4 xx (5/2)^(-2)`

Evaluate: `(4/5)^(-2) ÷ (4/5)^(-3)`

Evaluate: `2^7 xx (1/2)^(-3)`

Evaluate: (5⁰ + 6⁻¹) × 3³  

Evaluate: (2⁻¹ + 3⁻¹) ÷ 6⁻¹ 

Evaluate: (3⁻¹ + 4⁻² + 5⁻³)⁰ 

Simplify: (3²)³ × (2 × 3⁵)⁻² × (18)² 

Simplify: `(9^2 xx 7^3 xx 2^5)/(84^3)`

Simplify: `(2^8 xx 2187)/(3^5 xx 32)`

Solve for x: `(2^(2x - 1))/(2^(x + 2))` = 4

Solve for x: `(5^5 xx 5^(-4) xx 5^x)/(5^12)` = 5⁻⁵

Expand using exponents: 6054.321

Expand using exponents: 897.14

Find the number in standard form for the following expansions:

8 × 10⁴ + 7 × 10³ + 6 × 10² + 5 × 10¹ + 2 × 1 + 4 × 10⁻² + 7 × 10⁻⁴ 

Find the number in standard form for the following expansions:

5 × 10³ + 5 × 10¹ + 5 × 10⁻¹ + 5 × 10⁻³ 

Find the number in standard form for the following expansions:

The radius of a hydrogen atom is 2.5 × 10⁻¹¹ m 

Write the following numbers in scientific notation:

467800000000

Write the following numbers in scientific notation:

0.000001972

Write the following numbers in scientific notation:

1642.398

Write the following numbers in scientific notation:

Earth’s volume is about 1,083,000,000,000 cubic kilometres

Write the following numbers in scientific notation:

If you fill a bucket with dirt, the portion of the whole Earth that is in the bucket will be 0.0000000000000000000000016 kg

By what number should (−4)⁻¹ be multiplied so that the product becomes 10⁻¹?

(−2)⁻³ × (−2)⁻² = ____________

Which is not correct?

If `(10^x)/(10^(-3))` = 10⁹, then x is ____________

0.0000000002020 in scientific form is ____________

If `3/4` of a box of apples weighs 3 kg and 225 gm, how much does a full box of apples weigh?

Mangalam buys a water jug of capacity `3 4/5` litre. If she buys another jug which is `2 2/3` times as large as the smaller jug, how many litre can the larger one hold?

Ravi multiplied `25/8` and `16/15` to obtain `400/120`. He says that the simplest form of this product is `10/3` and Chandru says the answer in the simplest form is `3 1/3`. Who is correct? (or) Are they both correct? Explain

Find the length of a room whose area is `153/10` sq.m and whose breadth is `2 11/20` m

There is a large square portrait of a leader that covers an area of 4489 cm². If each side has a 2 cm liner, what would be its area?

A greeting card has an area 90 cm². Between what two whole numbers is the length of its side?

225 square shaped mosaic tiles, area 1 square decimeter exactly cover a square shaped verandah. How long is each side of the square shaped verandah?

If `root(3)(1906624) xx sqrt(x)` = 3100, find x

If 2^{m – 1} + 2^{m + 1} = 640, then find m

Give the answer in scientific notation:

A human heartbeats at an average of 80 beats per minute. How many times does it beat in an hour?

Give the answer in scientific notation:

A human heartbeats at an average of 80 beats per minute. How many times does it beat in a day?

Give the answer in scientific notation:

A human heartbeats at an average of 80 beats per minute. How many times does it beat in a year?

Give the answer in scientific notation:

A human heartbeats at an average of 80 beats per minute. How many times does it beat in 100 years?

In a map, if 1 inch refers to 120 km, then find the distance between two cities B and C which are `4 1/6` inches and `3 1/3` inches from the city A which lies between the cities B and C

Give an example and verify the following statement.

The collection of all non-zero rational numbers is closed under division

Give an example and verify the following statement.

Subtraction is not commutative for rational numbers

Give an example and verify the following statement.

Division is not associative for rational numbers

Give an example and verify the following statement.

Distributive property of multiplication over subtraction is true for rational numbers. That is, a(b – c) = ab – ac

Give an example and verify the following statement.

The mean of two rational numbers is rational and lies between them

If  `1/4` of a ragi adai weighs 120 grams, what will be the weight of `2/3` of the same ragi adai?

If p + 2q = 18 and pq = 40, find `2/"p" + 1/"q"`

Find x if `5 x/5 xx 3 3/4` = 21

By how much does `1/((10/11))` exceed `((1/10))/11`?

A group of 1536 cadets wanted to have a parade forming a square design. Is it possible? If it is not possible, how many more cadets would be required?

Evaluate: `sqrt(286225)` and use it to compute `sqrt(2862.25) + sqrt(28.6225)`

Simplify: (3.769 × 10⁵) + (4.21 × 10⁵)

Order the following from the least to the greatest: 16²⁵, 8¹⁰⁰, 3⁵⁰⁰, 4⁴⁰⁰, 2⁶⁰⁰