Unit 0 · Prereq

Arithmetic survival kit

Rounding, E-notation, percents, decimals, fractions, complements, divisibility

Practice 0/15Checkpoint best 0%

Rule cards

Look at the NEXT digit: 5 or more → round up; 4 or less → leave it.

Traps

Rounded at the wrong place value.
count places from the wrong side of the decimal point → wrong digit kept
✓ 12.8749 to 1 dp is 12.9, to 3 dp is 12.875
Chopped the extra digits instead of rounding.
12.8749 to 3 dp → chop the 9 → 12.874
✓ the next digit is 9 → round up → 12.875
Rounded one digit at a time from the right.
12.8749 → 12.875 → 12.88 → 12.9: only look at the one digit right after the place you keep
✓ 12.8749 to 2 dp is 12.87

E−k means × 10⁻ᵏ: move the decimal point k places LEFT and fill with zeros.

Traps

Moved the decimal right for a negative exponent.
3.8728E−4 → move right → 38728
✓ 3.8728E−4 = 0.00038728
Moved one place too few or too many.
9E−4 → write 3 zeros then 9 → 0.009
✓ 9E−4 = 0.0009; 1E−1 = 0.1
Read 1.8E−7 as 1.8 (or as a big number).
ignore the E part → probability 1.8 > 1 → impossible
✓ 1.8E−7 = 0.00000018 ≈ 0 → the event is unlikely

TI-84 Evo keys

Percent → decimal: move 2 left and drop %. Decimal → percent: move 2 right and add %. Multiply percents as decimals.

Adding or subtracting percents? Work with them directly: 28.8% − 12.6% + 35% = 51.2%.
Multiplying percents? Change each to a decimal first, multiply, then change back.

Traps

Moved the decimal only one place.
25.5% → 2.55
✓ 25.5% = 0.255; 0.257% = 0.00257
Multiplied the percent numbers as if they were whole numbers.
(3%)(5%) → 3 × 5 → 15%
✓ (3%)(5%) = (.03)(.05) = .0015 = 0.15%
Moved left when turning a decimal into a percent.
0.0065 → 0.000065%
✓ 0.0065 = 0.65%

Line up the decimal points and compare place by place from the left.

Traps

Thought the number with more digits is larger.
0.05 has more digits than 0.1 → 0.05 is bigger
✓ 0.1 > 0.05
Ignored the decimal point and compared the digit strings.
03245 vs 03255 → compared as whole numbers from the right
✓ 0.03245 < 0.03255 (the 4th decimal place decides)

Always reduce: divide top AND bottom by the same number.

Traps

Left the fraction unreduced.
12/52 left as is
✓ 12/52 = 3/13; 26/52 = 1/2; 15/216 = 5/72
Added the bottoms when adding fractions.
4/52 + 13/52 → 17/104
✓ same denominator → add the tops only: 4/52 + 13/52 − 1/52 = 16/52 = 4/13
Subtracted top and bottom separately in 1 − a/b.
1 − 5/6 → (1 − 5)/(1 − 6)
✓ 1 − a/b = (b − a)/b: 1 − 5/6 = 1/6; 1 − 9/17 = 8/17
Divided only one part of the fraction.
15/216 → divide the top by 5 and the bottom by 3 → 3/72
✓ divide BOTH by 3: 15/216 = 5/72

÷2: last digit even · ÷5: ends in 0 or 5 · ÷10: ends in 0 · ÷3 / ÷9: digit sum divisible by 3 / 9.

Traps

Used the last digit for the ÷3 or ÷9 test.
123 ends in 3 → divisible by 3 because of the 3
✓ ÷3 uses the digit SUM: 1 + 2 + 3 = 6 → yes
Assumed divisible by 3 means divisible by 9.
digit sum 6 → divisible by 3 → also by 9
✓ digit sum must be a multiple of 9 for ÷9

The complement is everything in the box that is NOT listed in the event.

Traps

Wrote the event instead of what is left over.
complement of {Red, Blue} → {Red, Blue}
✓ box {Orange, Red, Blue, Brown, Green}: complement of {Red, Blue} = {Orange, Brown, Green}
Missed one item of the box.
listed only {Orange, Green}
✓ check: event + complement = the whole box