Big and tiny, written tidily

Mathematics · Number Representation & Place Value · ages 15-16

Name ______________________ Date ____________

4.7 times 10 to the power k equals 0.00047. What is k?
Answer: ______________
Which is 5,600,000 in standard form?
- 5.6 × 10^6
- 5.6 × 10^5
- 56 × 10^6
- 0.56 × 10^5
Which is 5,600,000 in standard form?
- 5.6 times 10^6
- 56 times 10^5
- 5.6 times 10^5
34 times 10^5 is already in standard form.
Circle one: True False
What is (8 × 10^6) divided by (2 × 10^2)? Give the ordinary number.
Answer: ______________
Which is the standard form of 34 times 10^5?
- 3.4 times 10^5
- 34 times 10^6
- 3.4 times 10^6
What is (2 × 10^3) times (3 × 10^4) in standard form?
- 6 × 10^12
- 5 × 10^7
- 6 × 10^7
- 6 × 10^6
Maya says the leading number in standard form sits between 1 and 10. Is Maya right?
Circle one: True False
Zara multiplied (2 times 10^3) by (3 times 10^4) and wrote 6 times 10^12. What did she get wrong?
- She added the leaders
- She multiplied the powers
- She dropped a zero
0.09 × 10^3 in standard form is 9 × 10^k. What is k?
Answer: ______________

Answer key

For grown-ups. Fold this page away before handing over the rest.

-4 · The point slides 4 places left, so k = -4.
5.6 × 10^6 · 5.6 times a million is 5,600,000. The 5.6 times 10 to the 5 option is only 560,000.
5.6 times 10^6 · 5.6 times a million is 5,600,000. The 10^5 option is only 560,000.
False · The leader 34 exceeds 10. The fixed form is 3.4 times 10^6.
40000 · 8 over 2 = 4, powers 6 minus 2 = 4, so 4 times 10 to the 4 = 40000.
3.4 times 10^6 · Split 34 into 3.4 times 10, then merge: 10^6.
6 × 10^7 · 2 times 3 = 6, powers add 3 + 4 = 7. The 10 to the 12 option wrongly multiplies powers.
True · That range rule defines the form.
She multiplied the powers · Powers add in multiplication: 3 + 4 = 7, not 3 times 4 = 12.
1 · 0.09 times 1000 = 90 = 9 times 10, so k = 1.