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
- 14 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 14
Watch first
Standard form for very large and small numbers
An English teaching video on this topic from MathTalk. Watch it, then scroll down for the lesson.
In a nutshell
Interpret and compare numbers in standard form A x 10^n
Learning cycle
Part 2 of 14
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 14
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.
Explore the idea
Part 4 of 14
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 5 of 14
Quick check
What is 72,000 in standard form?
Reset break
Part 6 of 14
Pause
That's sitting 1 of 2 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.
Quick check
Part 7 of 14
Quick check
Which is larger, 3.5 × 10⁵ or 4.2 × 10⁴?
Learning cycle
Part 8 of 14
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 9 of 14
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 10 of 14
Quick check
In A × 10ⁿ, what must A satisfy?
Challenge round
Part 11 of 14
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 12 of 14
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.
Mastery quiz
Part 13 of 14
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 14 of 14
Lesson round-up
Ready when you are
Quiz score
Not sat
Games
Not played
Points this lesson
0
Best run
0 in a row
Luna: 0 out of 3 on the practice checks. Only if you feel up to it — one more?
Ask LunaDo the work
Your written work for this lesson
This is the part you'd do in your book at school. Pick the pieces below, write here or on paper, and photograph anything you draw or work out.
The cost of a school trip
A school is planning a trip to a wildlife park. The coach costs £480 however many people go. Entry costs £9.50 for each pupil and each adult goes free. The school says every pupil must pay the same amount, and the trip must not lose money.
If 60 pupils go, the coach works out at £8 each, so the total for each pupil is £17.50. If only 40 pupils go, the coach works out at £12 each, so the price rises to £21.50. The teacher explains that the coach is a fixed cost and the entry is a cost per person — which is why the price per pupil changes when the number changes.
The school decides to charge £20 and to use anything left over for a second trip later in the year.
Written for Good Learning Co.
Reading questions
- Work out the total cost of the trip if 50 pupils go.
- Show why the price per pupil falls when more pupils go, using numbers.
- At £20 each, how many pupils must go before the trip makes money? Show your working.
Working out
Working outDo the practice questions on paper, showing every step — not just the answer. Mark them yourself and circle anything you got wrong.
10–15 questions
Worked example, explained
WritingCopy one question out and write underneath, in words, why each step works.
1 question, 4–5 sentences
Problem in words
Working outWrite your own real-life problem that uses today's method, then solve it.
1 problem + solution
Saved as you type.
Part 1 of 14 · Watch & discover
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Interpret and compare numbers in standard form A x 10^n