Standard form for very large and small numbers
The Sun's mass has 30 digits before the decimal point — standard form squeezes it into something you can actually compare at a glance.
Part of your national curriculum
- Number: Interpret and compare numbers in standard form A x 10^n
Lesson overview
What you'll learn in this lesson
Interpret and compare numbers in standard form A x 10^n
Key learning points
- • The format
- • Worked example
- • Comparing
This lesson at a glance
- 26 minutes
- 17 parts to scroll through
- 3 quick checks
- Marked quiz at the end
- Gentle pace: short sittings with pauses
Words to know
Scroll down — the lesson carries on below
Watch & discover
Part 1 of 17
Visual introductionPicture this
Standard form for very large and small numbers
The Sun's mass has 30 digits before the decimal point — standard form squeezes it into something you can actually compare at a glance.
In a nutshell
Interpret and compare numbers in standard form A x 10^n
Learning cycle
Part 2 of 17
Learning cycle 1 of 2
Part 1 · The format
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 3 of 17
Learn
The format
Standard form writes a number as A × 10ⁿ, where 1 ≤ A < 10 and n is an integer. So 5,600,000 becomes 5.6 × 10⁶, and 0.00032 becomes 3.2 × 10⁻⁴.
Reset break
Part 4 of 17
Pause
That's sitting 1 of 4 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Explore the idea
Part 5 of 17
Learn
Worked example
Write 72,000 in standard form. Move the decimal point until only one non-zero digit remains before it: 7.2, and count 4 moves left, so 72,000 = 7.2 × 10⁴.
Quick check
Part 6 of 17
Quick check
Part 7 of 17
Reset break
Part 8 of 17
Pause
That's sitting 2 of 4 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Learning cycle
Part 9 of 17
Learning cycle 2 of 2
Part 2 · Comparing
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 10 of 17
Learn
Comparing
Compare 3.5 × 10⁵ and 4.2 × 10⁴. Convert both to ordinary numbers: 350,000 and 42,000. Since 350,000 is larger, 3.5 × 10⁵ is the bigger number.
Quick check
Part 11 of 17
Reset break
Part 12 of 17
Pause
That's sitting 3 of 4 done
Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.
Challenge round
Part 13 of 17
Game · Sort it
Which of these are true?
Drag each card into the right column. Tap a card first if dragging is fiddly.
True
Not true
Challenge round
Part 14 of 17
Game · Fill the gaps
Finish the sentences
Choose the word that belongs in each gap.
____ form writes a number as A × 10ⁿ, where 1 ≤ A < 10 and n is an integer.
Convert both to ordinary ____: 350,000 and 42,000.
Challenge round
Part 15 of 17
Game · Recall cards
What is 72,000 in standard form?
Card 1 of 3
Mastery quiz
Part 16 of 17
Marked quiz
End of lesson quiz: Standard form for very large and small numbers
3 questions, marked with the reasoning shown. No timer.
1. What is 72,000 in standard form?
2. Which is larger, 3.5 × 10⁵ or 4.2 × 10⁴?
3. In A × 10ⁿ, what must A satisfy?
Lesson round-up
Part 17 of 17
Lesson round-up
Ready when you are
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Ask LunaPart 1 of 17 · Watch & discover
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Interpret and compare numbers in standard form A x 10^n