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Multiply Numbers in Standard Form

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

'Multiply 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 multiply numbers in standard form, we add the powers of 10 and multiply the numbers on their own.

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

 

Example 1

Multiply together

5.1 x 106  x   3 x 104

 

Answer

5.1 x 3 = 15.3

106 x 104 = 1010

Answer is 15.3 x 1010 but this is not in standard form as 15.3 is greater than 10.

15.3 = 1.53 x 101

So answer is 1.53 x 1011

 

Example 2

Multiply together

5.2 x 106  x   9 x 10-4

 

Answer

5.2 x 9 = 46.8

106 x 10-4 = 102

Answer is 46.8 x 102 but this is not in standard form as 46.8 is greater than 10.

46.8 = 4.68 x 101

So answer is 4.68 x 103

Multiply together

 

4 x 106  x   6 x 104

 

(The answer must be in standard form)

24 x 1010

2.4 x 1011

2.4 x 1025

Multiply together

 

3 x 105  x   2 x 104

 

(The answer must be in standard form)

6 x 1020

5 x 1020

6 x 109

Multiply together

 

3 x 105  x   4 x 104

 

(The answer must be in standard form)

1.2 x 108

12 x 1020

1.2 x 1010

Multiply together

 

5 x 103  x   4 x 106

 

(The answer must be in standard form)

2 x 1010

20 x 1018

2.0 x 1018

Multiply together

 

1 x 10-3  x   4 x 106

 

(The answer must be in standard form)

4 x 103

5 x 10-18

4 x 1018

Multiply together

 

4 x 10-3  x   4 x 107

 

(The answer must be in standard form)

1.6 x 104

1.6 x 105

1.6 x 10-3

Multiply together

 

4.2 x 105  x   4 x 107

 

(The answer must be in standard form)

1.68 x 1012

1.68 x 1013

16.8 x 1012

Multiply together

 

6.3 x 105  x   3 x 10-7

 

(The answer must be in standard form)

1.89 x 10-12

18.9 x 1013

1.89 x 10-1

Multiply together

 

3.3 x 105  x   4 x 104

 

(The answer must be in standard form)

1.32 x 1010

13.2 x 1020

7.3 x 101

Multiply together

2.5 x 10-5  x   6 x 10-7

 

(The answer must be in standard form)

15 x 10-12

1.5 x 10-11

1.5 x 10-34

  • Question 1

Multiply together

 

4 x 106  x   6 x 104

 

(The answer must be in standard form)

CORRECT ANSWER
2.4 x 1011
EDDIE SAYS
24 × 1010 is not standard form
  • Question 2

Multiply together

 

3 x 105  x   2 x 104

 

(The answer must be in standard form)

CORRECT ANSWER
6 x 109
EDDIE SAYS
3 × 2 = 6
105 × 104 = 109
  • Question 3

Multiply together

 

3 x 105  x   4 x 104

 

(The answer must be in standard form)

CORRECT ANSWER
1.2 x 1010
EDDIE SAYS
12 × 109 is not standard form
  • Question 4

Multiply together

 

5 x 103  x   4 x 106

 

(The answer must be in standard form)

CORRECT ANSWER
2 x 1010
EDDIE SAYS
20 × 109 is not standard form
  • Question 5

Multiply together

 

1 x 10-3  x   4 x 106

 

(The answer must be in standard form)

CORRECT ANSWER
4 x 103
EDDIE SAYS
1 × 4 = 4
10-3 × 106 = 103
  • Question 6

Multiply together

 

4 x 10-3  x   4 x 107

 

(The answer must be in standard form)

CORRECT ANSWER
1.6 x 105
EDDIE SAYS
16 × 104 is not standard form
  • Question 7

Multiply together

 

4.2 x 105  x   4 x 107

 

(The answer must be in standard form)

CORRECT ANSWER
1.68 x 1013
EDDIE SAYS
16.8 × 1012 is not standard form
  • Question 8

Multiply together

 

6.3 x 105  x   3 x 10-7

 

(The answer must be in standard form)

CORRECT ANSWER
1.89 x 10-1
EDDIE SAYS
18.9 × 10-2 is not standard form
  • Question 9

Multiply together

 

3.3 x 105  x   4 x 104

 

(The answer must be in standard form)

CORRECT ANSWER
1.32 x 1010
EDDIE SAYS
13.2 × 109 is not standard form
  • Question 10

Multiply together

2.5 x 10-5  x   6 x 10-7

 

(The answer must be in standard form)

CORRECT ANSWER
1.5 x 10-11
---- OR ----

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