Standard form: large numbers

The Maths Habit

What number is this?

72000000000000000000

72 quintillion

Names of big numbers

Power of 10Number of zerosName todayOld British name
1066millionmillion
1099billionthousand million
101212trillionbillion
101515quadrillionthousand billion
101818quintilliontrillion
102121sextillionthousand trillion
102424septillionquadrillion
102727octillionthousand quadrillion
103030nonillionquintillion
Power of 10Number of zerosName todayOld British name
103333decillionthousand quintillion
103636undecillionsextillion
103939duodecillionthousand sextillion
104242tredecillionseptillion
104545quattuordecillionthousand septillion
108484quattuordecillion
10100100googolgoogol
10303303centillion
10600600centillion

Standard form

3.4 × 106 This number has to bebetween 1 and 10,not including 10. This number must be 10 This number mustbe an integer(a whole number)

Sort these into standard form and not standard form.

25 × 103✗7 × 103✓3.2 × 56✗2.5 × 104✓0.7 × 105✗9.9 × 102✓10 × 104✗1.08 × 106✓4.5 × 102.5✗6 × 108✓

Write 67 000 in standard form.

67 000 =6700× 10167 000 =670× 10267 000 =67× 103
Divide by 10, multiply by one more 10.
67 000 =6.7× 104

Write 380 000 in standard form

HThTThThHTO.th
ordinary
number		380000.
between
1 and 10		.

Write 67 000 in standard form.

67 000 =6700× 10167 000 =670× 10267 000 =67× 103
Divide by 10, multiply by one more 10.
67 000 =6.7× 104

Write 830 000 in standard form.

830 000 =83 000× 101830 000 =8300× 102830 000 =830× 103830 000 =83× 104
830 000 =8.3× 105

Write 67 000 in standard form.

67 000 =6700× 10167 000 =670× 10267 000 =67× 103
Divide by 10, multiply by one more 10.
67 000 =6.7× 104

Write 4700 in standard form.

4700 =470× 1014700 =47× 102
4700 =4.7× 103

Write 67 000 in standard form.

67 000 =6700× 10167 000 =670× 10267 000 =67× 103
Divide by 10, multiply by one more 10.
67 000 =6.7× 104

Write 52 000 in standard form.

52 000 =5200× 10152 000 =520× 10252 000 =52× 103
52 000 =5.2× 104

Write 67 000 in standard form.

67 000 =6700× 10167 000 =670× 10267 000 =67× 103
Divide by 10, multiply by one more 10.
67 000 =6.7× 104

Write 609 000 in standard form.

609 000 =6.09× 105

Write 67 000 in standard form.

67 000 =6700× 10167 000 =670× 10267 000 =67× 103
Divide by 10, multiply by one more 10.
67 000 =6.7× 104

Write 9 000 000 in standard form.

9 000 000 =9× 106

Standard form: large numbers worksheet, page 1

Write 3.4 × 105 as an ordinary number.

3.4 × 101 =343.4 × 102 =3403.4 × 103 =34003.4 × 104 =34 000
3.4 × 105 =340 000

Write 3.4 × 105 as an ordinary number.

3.4 × 101 =343.4 × 102 =3403.4 × 103 =34003.4 × 104 =34 000
3.4 × 105 =340 000

Write 6.1 × 103 as an ordinary number.

6.1 × 101 =616.1 × 102 =610
6.1 × 103 =6100

Write 3.4 × 105 as an ordinary number.

3.4 × 101 =343.4 × 102 =3403.4 × 103 =34003.4 × 104 =34 000
3.4 × 105 =340 000

Write 7.05 × 106 as an ordinary number.

7.05 × 106 =7 050 000

Which is bigger: 4.2 × 105 or 9.7 × 104?

4.2 × 105 = 420 000 9.7 × 104 = 97 000 420 000 is bigger, so 4.2 × 105 is bigger. Both are in standard form, so the bigger power of 10 is the bigger number.

Write these in order, smallest first: 3.5 × 104,  8 × 103,  3.05 × 104,  40 000

As ordinary numbers: 35 000,  8000,  30 500,  40 000 8 × 103,  3.05 × 104,  3.5 × 104,  40 000 The same power of 10? Compare the numbers in front: 3.05 is smaller than 3.5.

  1. Which is bigger: 9.8 × 104 or 1.2 × 105?

    1.2 × 105

  2. Ava writes 45 × 103. It is not in standard form. Write it correctly.

    4.5 × 104

Standard form: large numbers worksheet, page 2

Answer sheet

  1. The population of the UK is about 6.9 × 107. The population of France is about 68 000 000. Which country has more people?

    The UK (69 000 000)

  1. Write 72 000 in standard form.

    7.2 × 104

  2. Write 5.06 × 105 as an ordinary number.

    506 000

  3. 38 × 105 is not in standard form. Write it in standard form.

    3.8 × 106
Exit tickets to print

  1. Write 72 000 in standard form.

    7.2 × 104

  2. 38 × 105 is not in standard form. Write it in standard form.

    3.8 × 106

  3. Write 5.06 × 105 as an ordinary number.

    506 000

  4. Which is bigger, 4.1 × 106 or 9.8 × 105? Show how you know.

    4.1 × 106: 4 100 000
Exit tickets to print