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Divide Numbers in Standard Form

In this worksheet, students divide numbers written in standard form.

'Divide Numbers in Standard Form' worksheet

Key stage:  KS 4

Curriculum topic:  Number

Curriculum subtopic:  Calculate with Numbers in Standard Form A x 10n, Where 1 = A < 10 and n is An Integer

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

Standard (index) form is a shorthand way of writing a very large or a very small number.

It is written as a  number between 1 and 10 (but not equal to 10) multiplied by a power of 10, for example:


1.1223392 × 105 = 112233.92

6.94 x 10-4 = 0.000694

 

When we divide numbers in standard form, we subract the powers of 10 and divide the numbers on their own.

Then we must check that the answer is still in standard form and adjust if necessary.

 

Example 1

Divide

5.1 x 106  ÷   3 x 104

 

Answer

5.1 ÷ 3 = 1.7

106 ÷ 104 = 102

Answer is 1.7 x 102

 

Example 2

Divide

1.2 x 106  ÷   2.4 x 10-4

 

Answer

1.2 ÷ 2.4 = 0.5

106 ÷ 10-4 = 1010

Answer is 0.5 x 1010 but this is not in standard form as 0.5 is less than 1.

0.5 = 5 x 10-1

So answer is 5 x 109

Divide

 

4 x 106  ÷   2 x 104

 

(The answer must be in standard form)

2 x 101.5

2 x 102

8 x 1010

Divide

 

3 x 105  ÷   2 x 104

 

(The answer must be in standard form)

1 x 109

1.5 x 101

1.5 x 109

Divide

 

7.4 x 108  ÷   3.7 x 104

 

(The answer must be in standard form)

2 x 104

3.7 x 102

2 x 102

Divide

 

5 x 108  ÷   4 x 106

 

(The answer must be in standard form)

1.25 x 1014

20 x 1014

1.25 x 102

Divide

 

1 x 104  ÷   4 x 101

 

(The answer must be in standard form)

0.25 x 103

4 x 103

2.5 x 102

Divide

 

4 x 10-3  ÷   4 x 107

 

(The answer must be in standard form)

1 x 10-10

8 x 104

1 x 104

Divide

 

4.2 x 105  ÷   4 x 107

 

(The answer must be in standard form)

1.05 x 10-2

1.15 x 10-2

0.2 x 1012

Divide

 

6.3 x 105  ÷   3 x 10-7

 

(The answer must be in standard form)

2.1 x 10-12

6 x 1013

2.1 x 1012

Divide

 

1.65 x 105  ÷   3 x 10-7

 

(The answer must be in standard form)

0.55 x 1012

5.5 x 1011

5.5 x 1013

Divide

 

1.24 x 10-5  ÷   8 x 107

 

(The answer must be in standard form)

0.155 x 10-12

1.55 x 10-11

1.55 x 10-13

  • Question 1

Divide

 

4 x 106  ÷   2 x 104

 

(The answer must be in standard form)

CORRECT ANSWER
2 x 102
EDDIE SAYS
4 ÷ 2 = 2
106 ÷ 104 = 102
  • Question 2

Divide

 

3 x 105  ÷   2 x 104

 

(The answer must be in standard form)

CORRECT ANSWER
1.5 x 101
EDDIE SAYS
3 ÷ 2 = 1.5
105 ÷ 104 = 101
  • Question 3

Divide

 

7.4 x 108  ÷   3.7 x 104

 

(The answer must be in standard form)

CORRECT ANSWER
2 x 104
EDDIE SAYS
7.4 ÷ 3.7 = 2
108 ÷ 104 = 104
  • Question 4

Divide

 

5 x 108  ÷   4 x 106

 

(The answer must be in standard form)

CORRECT ANSWER
1.25 x 102
EDDIE SAYS
5 ÷ 4 = 1.25
108 ÷ 106 = 102
  • Question 5

Divide

 

1 x 104  ÷   4 x 101

 

(The answer must be in standard form)

CORRECT ANSWER
2.5 x 102
EDDIE SAYS
0.25 × 103 is not standard form
  • Question 6

Divide

 

4 x 10-3  ÷   4 x 107

 

(The answer must be in standard form)

CORRECT ANSWER
1 x 10-10
EDDIE SAYS
4 ÷ 4 = 1
10-3 ÷ 107 = 10-10
  • Question 7

Divide

 

4.2 x 105  ÷   4 x 107

 

(The answer must be in standard form)

CORRECT ANSWER
1.05 x 10-2
EDDIE SAYS
4.2 ÷ 4 = 1.05
105 ÷ 107 = 10-2
  • Question 8

Divide

 

6.3 x 105  ÷   3 x 10-7

 

(The answer must be in standard form)

CORRECT ANSWER
2.1 x 1012
EDDIE SAYS
6.3 ÷ 3 = 2.1
105 ÷ 10-7 = 1012
  • Question 9

Divide

 

1.65 x 105  ÷   3 x 10-7

 

(The answer must be in standard form)

CORRECT ANSWER
5.5 x 1011
EDDIE SAYS
0.55 × 1012 is not standard form
  • Question 10

Divide

 

1.24 x 10-5  ÷   8 x 107

 

(The answer must be in standard form)

CORRECT ANSWER
1.55 x 10-13
EDDIE SAYS
0.155 × 10-12 is not standard form
---- OR ----

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