Practice: Estimation and rounding

Estimation and rounding

Warm-upHuman

Round $4372$ to the nearest hundred.

Estimation and rounding

Warm-upHuman

Round $2950$ to the nearest hundred.

Estimation and rounding

CoreHuman

Round $3.46$ to the nearest tenth.

Choose one

3.5

3.4

3

4

Estimation and rounding

CoreHuman

Kwame's calculator says $39 \times 61 = 1379$ . Which is the best quick check?

Choose one

39 \times 61 \approx 40 \times 60 = 2400

, so

1379

must be wrongCalculators are never wrong, so it must be right

39 + 61 = 100

, so the answer should be about

100

It ends in

9

, and

9 \times 1 = 9

, so it is right

Estimation and rounding

CoreHuman

You know that $30 \le a \le 40$ and $20 \le b \le 30$ . What is the largest possible value of $a - b$ ?

Estimation and rounding

CoreHuman

Wanjiru has $1000$ shillings. The prices are $289$ , $412$ and $198$ shillings. Which reasoning shows for certain that she has enough money, without adding exactly?

Choose one

Each price is at most

300

,

500

and

200

, and

300 + 500 + 200 = 1000

The prices round to

300

,

400

and

200

, and

900

is less than

1000

Each price is at least

200

,

400

and

100

, and

700

is less than

1000

Three prices that each have three digits always add up to less than

1000

Estimation and rounding

CoreHuman

Work out $14 + 14 + 14$ in two ways: (1) round each $14$ to the nearest ten and add; (2) add exactly, then round the total to the nearest ten. What happens?

Choose one

Way (1) gives

30

and way (2) gives

40

: they differBoth ways give

40

Both ways give

30

Way (1) gives

40

and way (2) gives

30

Estimation and rounding

StretchHuman

Ama rounds $2.45$ to the nearest tenth and gets $2.5$ . Then she rounds $2.5$ to the nearest whole number and gets $3$ . What is $2.45$ rounded directly to the nearest whole number?

Choose one

2

3

2.5

Estimation and rounding

CoreFormal

In Lean, roundTen n is $n$ rounded to the nearest ten. Gideon wants to state precisely that rounding to the nearest ten changes $n$ by at most $5$ . Which statement says that?

Choose one

roundTen n ≤ n + 5 ∧ n ≤ roundTen n + 5roundTen n = nroundTen n ≤ 5roundTen n ≤ n + 5

Estimation and rounding

StretchComputational

Write round_to(n, place) that rounds a whole number n to the nearest place (10, 100, 1000, …) using the school rule, so that halfway rounds up. The starter uses Python's built-in round(), which rounds halves to even, so some tests fail. Use whole-number arithmetic instead: add half of place, then knock off the lower digits with //.

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