One-page revision sheet

• 10¹ = 10, 10² = 100, 10³ = 1000, 10⁴ = 10 000 — the index is the number of zeros.
• Multiplying by 10ⁿ moves every digit n places to the left. The number gets bigger.
• Dividing by 10ⁿ moves every digit n places to the right. The number gets smaller.
• It is the digits that move, not the decimal point — but moving the point the other way gives the same result, so either picture works.
• Fill any empty places with zeros: 4.5 × 10³ = 4500, and 47 ÷ 10³ = 0.047.
• “Crossing off zeros” only works if the number has enough zeros to cross off, so it is safer to move the digits.
• Always sanity-check: should the answer be bigger or smaller than you started with?

Key words: power of 10  ·  index  ·  place value  ·  decimal point  ·  digit

• The method is the same for every degree of accuracy.
• Find the digit in the rounding position, then look at the digit immediately to its right.
• If that digit is 5 or more, increase the rounding digit by 1.
• If it is less than 5, leave the rounding digit as it is.
• Then drop everything after the rounding position.
• Rounding up can carry: 9.999 to 2 d.p. is 10.
• For a division, work out one more decimal place than you need, then round.
• Round once, from the original number — rounding in stages can give the wrong answer.

Key words: round  ·  degree of accuracy  ·  decimal place  ·  significant figures