Calculating with standard form

The Maths Habit

1Write 500 in standard form.5 × 102
2Write 7000 in standard form.7 × 103
3Write 3 × 102 as an ordinary number.300
4Write 6 × 104 as an ordinary number.60 000

Lena types this on her calculator. What does the display mean?

200000×300000=
6×1010

6 × 1010 = 60 000 000 000. It is too long for the screen, so the calculator uses standard form.

Standard form
A number between 1 and 10, times a power of 10.
number × 10power
between 1 and 10
Power
The small number up high. It counts the tens multiplied.
10
×10ˣ key
The calculator key for × 10 to a power. On some calculators it says EXP.
×10x
Display
The screen on a calculator. It shows the answer.
 

Type 3 × 104 on your calculator. Copy the display.

1Type the number. Use the ×10ˣ key.
3×10x4=
2Copy the display.
30 000

Type 5 × 102 on your calculator. Copy the display.

1Type the number. Use the ×10ˣ key.
5×10x2=
2Copy the display.
500

Type 3 × 104 on your calculator. Copy the display.

1Type the number. Use the ×10ˣ key.
3×10x4=
2Copy the display.
30 000
1Type the number. Use the ×10ˣ key.2Copy the display.

Type 2 × 103 on your calculator. Copy the display.

1Type the number. Use the ×10ˣ key.
2×10x3=
2Copy the display.
2000

Type 3 × 104 on your calculator. Copy the display.

1Type the number. Use the ×10ˣ key.
3×10x4=
2Copy the display.
30 000
1Type the number. Use the ×10ˣ key.2Copy the display.

Type 7 × 101 on your calculator. Copy the display.

1Type the number. Use the ×10ˣ key.
7×10x1=
2Copy the display.
70

Type 3 × 104 on your calculator. Copy the display.

1Type the number. Use the ×10ˣ key.
3×10x4=
2Copy the display.
30 000
1Type the number. Use the ×10ˣ key.2Copy the display.

Type 4 × 105 on your calculator. Copy the display.

1Type the number. Use the ×10ˣ key.
4×10x5=
2Copy the display.
400 000

Work out (2 × 101) × (3 × 102)

1Type the numbers. Use the ×10ˣ key.
2×10x1×3×10x2=
2Copy the display.
6000
3Write it in standard form.
6000=600× 10=60× 10 × 10=6× 10 × 10 × 10=6× 103

Work out (2 × 101) × (4 × 101)

1Type the numbers. Use the ×10ˣ key.
2×10x1×4×10x1=
2Copy the display.
800
3Write it in standard form.
800=80× 10=8× 10 × 10=8× 102

Work out (2 × 101) × (3 × 102)

1Type the numbers. Use the ×10ˣ key.
2×10x1×3×10x2=
2Copy the display.
6000
3Write it in standard form.
6000=600× 10=60× 10 × 10=6× 10 × 10 × 10=6× 103
1Type the numbers. Use the ×10ˣ key.2Copy the display.3Write it in standard form.

Work out (4 × 101) × (1 × 102)

1Type the numbers. Use the ×10ˣ key.
4×10x1×1×10x2=
2Copy the display.
4000
3Write it in standard form.
4000=400× 10=40× 10 × 10=4× 10 × 10 × 10=4× 103

Work out (2 × 101) × (3 × 102)

1Type the numbers. Use the ×10ˣ key.
2×10x1×3×10x2=
2Copy the display.
6000
3Write it in standard form.
6000=600× 10=60× 10 × 10=6× 10 × 10 × 10=6× 103
1Type the numbers. Use the ×10ˣ key.2Copy the display.3Write it in standard form.

Work out (3 × 101) × (1 × 101)

1Type the numbers. Use the ×10ˣ key.
3×10x1×1×10x1=
2Copy the display.
300
3Write it in standard form.
300=30× 10=3× 10 × 10=3× 102

Work out (2 × 101) × (3 × 102)

1Type the numbers. Use the ×10ˣ key.
2×10x1×3×10x2=
2Copy the display.
6000
3Write it in standard form.
6000=600× 10=60× 10 × 10=6× 10 × 10 × 10=6× 103
1Type the numbers. Use the ×10ˣ key.2Copy the display.3Write it in standard form.

Work out (9 × 101) × (1 × 102)

1Type the numbers. Use the ×10ˣ key.
9×10x1×1×10x2=
2Copy the display.
9000
3Write it in standard form.
9000=900× 10=90× 10 × 10=9× 10 × 10 × 10=9× 103

Calculating with standard form worksheet, page 1

Calculating with standard form worksheet, page 2

Answer sheet

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

  1. (2 × 102) × (3 × 101) = 6000

    Right

  2. 800 = 8 × 103

    Wrong: 800 = 8 × 102

  3. To type 4 × 103, press 4 ×10ˣ 3

    Right

  4. (1 × 102) × (4 × 101) = 4 × 102

    Wrong: it is 4000 = 4 × 103

  5. (3 × 101) × (2 × 101) = 6 × 102

    Right

  1. Without a calculator: work out (3 × 105) × (2 × 106). Multiply the numbers. Add the powers.

    6 × 1011

  2. Without a calculator: work out (6 × 109) ÷ (2 × 104). Divide the numbers. Subtract the powers.

    3 × 105

  3. Jo gets 20 × 105. Why is it not standard form? Write it in standard form.

    2 × 106

  1. Work out
    (2 × 101) × (3 × 101)

    6 × 102
    1×10x×10x23=× 10=× 10 × 10=× 10

  2. Work out
    (3 × 101) × (3 × 101)

    9 × 102
    123=× 10=× 10 × 10=× 10

  3. Work out (1 × 102) × (7 × 101) in standard form.

    7 × 103
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