Standard form: large numbers

The Maths Habit

Work out.

110 × 10= 100
210 × 10 × 10= 1000
33 × 100= 300
44 × 1000= 4000

Which number is bigger? How do you know?

A400000000B90000000

A. It has more digits: 400 million. Counting zeros is slow. Standard form counts them for you.

Power of 10
10 multiplied by itself.
10 × 10 × 10
Power
The small number up high. It counts the tens multiplied.
10
Standard form
A number between 1 and 10, times a power of 10.
number × 10power
between 1 and 10
Ordinary number
A number written the usual way, with all its digits.
000

Write 1000 as a power of 10.

1Write the tens.
1000 = 10 × 10 × 10
2Count the tens.
1000 = 103

Write 100 as a power of 10.

1Write the tens.
100 = 10 × 10
2Count the tens.
100 = 102

Write 1000 as a power of 10.

1Write the tens.
1000 = 10 × 10 × 10
2Count the tens.
1000 = 103
1Write the tens.2Count the tens.

Write 10 000 as a power of 10.

1Write the tens.
10 000 = 10 × 10 × 10 × 10
2Count the tens.
10 000 = 104

Write 1000 as a power of 10.

1Write the tens.
1000 = 10 × 10 × 10
2Count the tens.
1000 = 103
1Write the tens.2Count the tens.

Write 10 as a power of 10.

1Write the tens.
10 = 10
2Count the tens.
10 = 101

Write 1000 as a power of 10.

1Write the tens.
1000 = 10 × 10 × 10
2Count the tens.
1000 = 103
1Write the tens.2Count the tens.

Write 100 000 as a power of 10.

1Write the tens.
100 000 = 10 × 10 × 10 × 10 × 10
2Count the tens.
100 000 = 105

Write 2000 in standard form.

1Divide by 10, multiply by one more 10.
2000 =200× 102000 =20× 10 × 10
2Stop when the number in front is 1 to 9.
2000 =2× 10 × 10 × 10
3Count the tens.
2000 =2× 103

Write 300 in standard form.

1Divide by 10, multiply by one more 10.
300 =30× 10
2Stop when the number in front is 1 to 9.
300 =3× 10 × 10
3Count the tens.
300 =3× 102

Write 2000 in standard form.

1Divide by 10, multiply by one more 10.
2000 =200× 102000 =20× 10 × 10
2Stop when the number in front is 1 to 9.
2000 =2× 10 × 10 × 10
3Count the tens.
2000 =2× 103
1Divide by 10, multiply by one more 10.2Stop when the number in front is 1 to 9.3Count the tens.

Write 5000 in standard form.

1Divide by 10, multiply by one more 10.
5000 =500× 105000 =50× 10 × 10
2Stop when the number in front is 1 to 9.
5000 =5× 10 × 10 × 10
3Count the tens.
5000 =5× 103

Write 2000 in standard form.

1Divide by 10, multiply by one more 10.
2000 =200× 102000 =20× 10 × 10
2Stop when the number in front is 1 to 9.
2000 =2× 10 × 10 × 10
3Count the tens.
2000 =2× 103
1Divide by 10, multiply by one more 10.2Stop when the number in front is 1 to 9.3Count the tens.

Write 70 in standard form.

1Divide by 10, multiply by one more 10.
2Stop when the number in front is 1 to 9.
70 =7× 10
3Count the tens.
70 =7× 101

Write 2000 in standard form.

1Divide by 10, multiply by one more 10.
2000 =200× 102000 =20× 10 × 10
2Stop when the number in front is 1 to 9.
2000 =2× 10 × 10 × 10
3Count the tens.
2000 =2× 103
1Divide by 10, multiply by one more 10.2Stop when the number in front is 1 to 9.3Count the tens.

Write 800 in standard form.

1Divide by 10, multiply by one more 10.
800 =80× 10
2Stop when the number in front is 1 to 9.
800 =8× 10 × 10
3Count the tens.
800 =8× 102

Standard form: large numbers worksheet, page 1

Standard form: large numbers worksheet, page 2

Answer sheet

Is it right?
Thumbs up: right. Thumbs down: wrong.

  1. 5000 = 5 × 103

    Right

  2. 30 000 = 3 × 105

    Wrong: 30 000 = 3 × 104

  3. 9 × 103 = 9000

    Right

  4. 6 × 102 = 60

    Wrong: 6 × 102 = 600

  5. 10 = 1 × 101

    Right

  1. Write 600 000 in standard form.

    6 × 105

  2. Which is bigger, 9 × 104 or 1 × 105?

    1 × 105 (100 000)

  3. Write 45 000 in standard form.

    4.5 × 104 (4.5 is between 1 and 10)

  1. Write 6000 in standard form.

    6 × 103
    6000 =600× 1016000 =× 10 × 106000 =× 10 × 10 × 1026000 =× 1031Divide by 10,multiply byone more 10.2Stop when thenumber in frontis 1 to 9.3Count thetens.

  2. Write 800 in standard form.

    8 × 102
    800 =× 101800 =× 10 × 102800 =× 1031Divide by 10,multiply byone more 10.2Stop when thenumber in frontis 1 to 9.3Count thetens.

  3. Write 90 000 in standard form.

    9 × 104
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