Foundation and Higher · standard form

Standard form.
Count the hops.

big numbers positive,
small numbers negative

always written the same way —

A × 10ⁿ

A is between 1 and 10

n counts the decimal point hops

step 1 of 4

A big number

1. Point after the first digit: 4.5.

2. Count the hops back to the start: 4.

✓ 45 000 = 4.5 × 10⁴

step 2 of 4

A small number

1. Point after the first non-zero: 3.2.

2. 3 hops the other way: negative power.

✓ 0.0032 = 3.2 × 10⁻³

step 3 of 4

Back to ordinary

1. Positive power: the number gets bigger.

2. Hop right 5 times. Fill gaps with zeros.

✓ A negative power hops left instead

6.1 × 10⁵

= 6.1 × 100 000 5 hops right

= 610 000

step 4 of 4

Multiplying

1. Multiply the numbers. Add the powers.

2. 15 is too big: write it as 1.5 × 10.

✓ Always check A is between 1 and 10

(5 × 10⁴) × (3 × 10³)

= 15 × 10⁷ 5 × 3, then 4 + 3

= 1.5 × 10⁸ 15 is too big

standard form —

A × 10ⁿ

A is at least 1, less than 10

Big number

positive power

Small number

negative power

Multiplying: multiply the numbers,
add the powers, then check A.

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