Standard form: small numbers

The Maths Habit

What number is this?

0.000000001

One billionth

Names of small numbers

Power of 10Number of zerosNamePrefix
10−11one tenthdeci
10−22one hundredthcenti
10−33one thousandthmilli
10−66one millionthmicro
10−99one billionthnano
10−1212one trillionthpico
Power of 10Number of zerosNamePrefix
10−1515one quadrillionthfemto
10−1818one quintillionthatto
10−2121one sextillionthzepto
10−2424one septillionthyocto
10−2727one octillionthronto
10−3030one nonillionthquecto

Standard form

3.4 × 10−6 This number has to bebetween 1 and 10,not including 10. This number must be 10 This number mustbe an integer(a whole number)

Negative index
A negative power of 10 makes a number smaller than 1.

Sort these into standard form and not standard form.

25 × 10−4✗2.5 × 10−3✓0.6 × 10−2✗7 × 10−5✓10 × 10−3✗1.04 × 10−2✓4.2 × 10−1.5✗3 × 5−2✗9.9 × 10−8✓6.6 × 10−1✓

Write 0.00036 in standard form.

0.00036 =0.0036÷ 1010.00036 =0.036÷ 1020.00036 =0.36÷ 1030.00036 =3.6÷ 104
Multiply by 10, divide by one more 10.
÷ 104 is the same as × 10−4
0.00036 =3.6× 10−4

Write 0.00029 in standard form

O.ththtthhth
ordinary
number		0.00029
between
1 and 10		.

Write 0.00036 in standard form.

0.00036 =0.0036÷ 1010.00036 =0.036÷ 1020.00036 =0.36÷ 1030.00036 =3.6÷ 104
Multiply by 10, divide by one more 10.
÷ 104 is the same as × 10−4
0.00036 =3.6× 10−4

Write 0.0091 in standard form.

0.0091 =0.091÷ 1010.0091 =0.91÷ 1020.0091 =9.1÷ 103
0.0091 =9.1× 10−3

Write 0.00036 in standard form.

0.00036 =0.0036÷ 1010.00036 =0.036÷ 1020.00036 =0.36÷ 1030.00036 =3.6÷ 104
Multiply by 10, divide by one more 10.
÷ 104 is the same as × 10−4
0.00036 =3.6× 10−4

Write 0.064 in standard form.

0.064 =0.64÷ 1010.064 =6.4÷ 102
0.064 =6.4× 10−2

Write 0.00036 in standard form.

0.00036 =0.0036÷ 1010.00036 =0.036÷ 1020.00036 =0.36÷ 1030.00036 =3.6÷ 104
Multiply by 10, divide by one more 10.
÷ 104 is the same as × 10−4
0.00036 =3.6× 10−4

Write 0.0072 in standard form.

0.0072 =0.072÷ 1010.0072 =0.72÷ 1020.0072 =7.2÷ 103
0.0072 =7.2× 10−3

Write 0.00036 in standard form.

0.00036 =0.0036÷ 1010.00036 =0.036÷ 1020.00036 =0.36÷ 1030.00036 =3.6÷ 104
Multiply by 10, divide by one more 10.
÷ 104 is the same as × 10−4
0.00036 =3.6× 10−4

Write 0.09 in standard form.

0.09 =0.9÷ 1010.09 =9÷ 102
0.09 =9× 10−2

Write 0.00036 in standard form.

0.00036 =0.0036÷ 1010.00036 =0.036÷ 1020.00036 =0.36÷ 1030.00036 =3.6÷ 104
Multiply by 10, divide by one more 10.
÷ 104 is the same as × 10−4
0.00036 =3.6× 10−4

Write 0.000805 in standard form.

0.000805 =0.00805÷ 1010.000805 =0.0805÷ 1020.000805 =0.805÷ 1030.000805 =8.05÷ 104
0.000805 =8.05× 10−4

Standard form: small numbers worksheet, page 1

Write 4.7 × 10−3 as an ordinary number.

× 10−3 means ÷ 103
4.7 ÷ 101 =0.474.7 ÷ 102 =0.047
4.7 × 10−3 =0.0047

Write 4.7 × 10−3 as an ordinary number.

× 10−3 means ÷ 103
4.7 ÷ 101 =0.474.7 ÷ 102 =0.047
4.7 × 10−3 =0.0047

Write 8 × 10−2 as an ordinary number.

× 10−2 means ÷ 102
8 ÷ 101 =0.8
8 × 10−2 =0.08

Write 4.7 × 10−3 as an ordinary number.

× 10−3 means ÷ 103
4.7 ÷ 101 =0.474.7 ÷ 102 =0.047
4.7 × 10−3 =0.0047

Write 1.95 × 10−4 as an ordinary number.

1.95 × 10−4 =0.000195

Which is smaller: 3.6 × 10−4 or 8.1 × 10−5?

3.6 × 10−4 = 0.00036 8.1 × 10−5 = 0.000081 0.000081 is smaller, so 8.1 × 10−5 is smaller. 10−5 is smaller than 10−4: the more negative the power, the smaller the number.

Write these in order, smallest first: 4.5 × 10−3,  7 × 10−4,  4.05 × 10−3,  0.004

As ordinary numbers: 0.0045,  0.0007,  0.00405,  0.004 7 × 10−4,  0.004,  4.05 × 10−3,  4.5 × 10−3 The same power of 10? Compare the numbers in front: 4.05 is smaller than 4.5.

  1. Which is the smallest:   3 × 10−4,   5 × 10−5   or   2 × 10−3?

    5 × 10−5

  2. Write 0.25 × 10−2 in standard form.

    2.5 × 10−3

Standard form: small numbers worksheet, page 2

Answer sheet

  1. A grain of salt is about 3 × 10−4 m across. A grain of fine sand is about 0.0002 m across. Which grain is smaller?

    The sand (0.0002 m)

  1. Write 0.0047 in standard form.

    4.7 × 10−3

  2. Write 6.08 × 10−4 as an ordinary number.

    0.000608

  3. Which is the smallest: 7 × 10−3, 2 × 10−2 or 9 × 10−4?

    9 × 10−4
Exit tickets to print

  1. Write 0.0047 in standard form.

    4.7 × 10−3

  2. Leo writes 0.0063 as 6.3 × 103. Write it correctly.

    6.3 × 10−3

  3. Write 6.08 × 10−4 as an ordinary number.

    0.000608

  4. Which is the smallest: 7 × 10−3, 2 × 10−2 or 9 × 10−4?

    9 × 10−4
Exit tickets to print