Standard Form

Scientific Notation

Uganda Primary 7 Mathematics
Topic 3 — Term I

Numbers That Are Hard to Write

Which column is easier?

The Same Numbers — Standard Form

Can you see the pattern?

• The part before is between 1 and 10
• The exponent tells you how many places the decimal moved

The Definition of Standard Form

Standard form is written as:

where:

• — one non-zero digit before the point
• is a whole number

Examples:

• ✓
• ✓
• ✓

Is It Standard Form? Check A

All equal ; only the first is standard.

Fixing Non-Standard Expressions Into Standard Form

Rule: each decimal move in changes by .

• Decimal left (smaller ): increase by 1
• Decimal right (larger ): decrease by 1

Expanded Form vs Standard Form — Comparison

The same number, 47,000, in three representations:

Expanded form: one term per digit. Standard form: one term total.

The Decimal-Point Method for Conversion

To convert a whole number to standard form:

1. Locate the decimal point at the right end
2. Move it left until one digit remains left
3. Count the moves — the exponent
4. Write ; do the A-check

Worked Example 1 — 64,000,000

Move decimal 7 places left:

A-check: , and ✓

Verify: ✓

Worked Example 2 — 5,030,000

Move decimal 6 places left:

Internal zero is preserved in — not .

A-check: , ✓

Worked Example 3 — 900

Move decimal 2 places left:

A-check: , ✓

Useful rule: A number with zeros and a single leading digit gives .

Misconception 1: Stopping One Move Early

Error: ✗

Check: Is ? Yes — not standard form.

Fix: One more move left:

Always do the A-check last before writing your final answer.

Misconception 2 — Counting Zeros Instead of Moves

Error: ✗ (counted 6 zeros as 7)

Correct method — count decimal moves:

Six moves, not seven. The A-check also confirms: .

Your Turn — Convert to Standard Form

Convert these to standard form:

For each: count the decimal moves, write , apply the A-check.

Reverse Direction — Decimal Moves Right

To convert to an ordinary number:

1. Write with its decimal point
2. Move the decimal point right by exactly places
3. Fill empty positions with zeros

Worked Example 4 —

Verify: ?
Move decimal 5 left from : ✓

Worked Example 5 —

Internal zero is preserved — fills the hundred-thousands position.

Worked Example 6 —

For A without decimals: just append zeros after the digit.

Your Turn — Convert to Ordinary Form

Convert to ordinary numbers:

Then verify by converting your answer back to standard form.

Round-Trip Verification of Both Directions

If the round-trip gives back the starting number, both conversions are correct.

Lesson Summary — Rule Card

Always A-check: confirm .