How do you round to the nearest ten?

Look at the ones digit. 5 or more rounds up to the next ten; 4 or less rounds down. 47 rounds to 50, 43 rounds to 40, and 45 - exactly halfway - rounds up to 50 by convention. Only the single digit to the right of the place you are rounding to decides.

The digits 1-4 are nearer the lower ten and 6-9 are nearer the upper one, so they choose themselves. 5 is exactly halfway, and a tie needs a convention; schools and most everyday arithmetic settle it upward so everyone gets the same answer. It is a chosen rule for the one case distance cannot decide.

How do you estimate 38 x 52 quickly?

Round each number to something friendly and multiply: 38 x 52 is roughly 40 x 50 = 2000. The true answer is 1976, so the estimate lands within about one percent. Rounding one number up and the other down is the professional touch - the two errors partly cancel.

What is estimation for?

Knowing the size of an answer before working it out, so a slip announces itself. If you expect roughly 2000 and your careful calculation says 19,760, a dropped decimal point has nowhere to hide. Estimation is not lazy arithmetic - it is the checking layer that makes exact arithmetic trustworthy.

Estimation and Rounding

Here is a superpower disguised as a shortcut: knowing the size of an answer before you work it out. Estimate first and a slipped decimal point has nowhere to hide — you expected about 2,000, the calculator says 19,760, and the alarm rings itself. This guide teaches rounding step by step, then how to spend it on estimates that land startlingly close.

Rounding whole numbers

To the nearest ten: one digit decides

Find the tens on either side. (For 47: 40 and 50.)
Look at the ones digit only. 5 or more → up. 4 or less → down.

47 → 50. 43 → 40. 45 → 50 (halfway rounds up).

Why does 5 round up? 1–4 are nearer the lower ten, 6–9 nearer the upper — they choose themselves. 5 is EXACTLY halfway, and distance cannot break the tie, so a convention does. Everyone rounding halfway the same direction is worth more than the direction chosen.

To the nearest hundred or thousand: same rule, one place along

The digit one place to the right of the target decides — and only that digit.

1,860 to the nearest hundred → the tens digit is 6 → 1,900.

3,485 to the nearest thousand → the hundreds digit is 4 → 3,000. (Yes, down — the 85 does not get a vote.)

3,485 sits between 3,000 and 4,000, and it is 485 in — less than halfway. The single deciding digit is a shortcut for "which side of halfway?", which is why digits further right never matter: they cannot drag the number across the halfway line once the deciding digit has spoken.

Rounding decimals: the same rule again

4.56 to one decimal place → next digit 6 → 4.6. 7.43 to the nearest whole → next digit 4 → 7.

More on decimal places in the decimals guide.

Estimating: rounding with a purpose

Step by step

Round each number to one friendly digit (its front digit, usually).
Do the now-easy calculation in your head.
Say the answer with an honest "about".

38 × 52 ≈ 40 × 50 = 2,000 (true answer 1,976 — within about 1%).

487 + 512 ≈ 500 + 500 = 1,000 (true answer 999. Sometimes the universe smiles.)

The professional touch: one up, one down

When you round both numbers the same way, the errors stack. Round one up and one down and they partly cancel — 38 × 52 rounds 38 up to 40 and 52 down to 50, which is why the estimate lands so close.

Multiplication magnifies: an error in a factor scales the whole answer, so opposite-direction errors fight each other while same-direction errors gang up. This one habit is most of the difference between a rough guess and a tight estimate.

Sanity checks: the estimate as a bodyguard

Before accepting any careful answer, ask what size it should be. A restaurant bill of £87 split four ways should be "a bit over £20 each" — if long division hands you £217.50, the estimate catches it instantly. This works on units too: a door 2 meters tall is plausible; a door 2 centimeters tall is a cat flap for a mouse.

Rounding to COMPUTE (a different trick, worth knowing apart)

Rounding also powers an exact method: add the friendly number, then give back the change.

348 + 99 → 348 + 100 − 1 = 447. Exact, not an estimate.

Both tricks round; the difference is honesty about the leftover. Estimation throws the leftover away and says "about". Rounding-and-adjusting keeps the leftover and pays it back, so the answer stays exact. Knowing which one you are doing is the skill. More like this in mental math tricks.

A word on significant figures

Later on, "round to the nearest hundred" grows up into "round to 2 significant figures" — counting digits from the first nonzero one, so 0.004718 to 2 s.f. is 0.0047. Same deciding-digit rule, new way of naming the cut. The app's Significant Figures lesson takes it from there.

The three mistakes worth naming

Letting far-right digits vote. 3,485 to the nearest thousand is 3,000 — the 85 cannot drag it across halfway.
Rounding both numbers the same way in a product. Errors stack; go one up, one down.
Serving an estimate as exact. ≈ earns its keep by being honest — 40 × 50 tells you 1,976 is plausible, not that it is 2,000.

Learn it properly in the app

Each move above is a lesson in Math Challenge, with pictures and try-it problems. The first four need no purchase:

Rounding to the Nearest Ten — round to the nearer ten; halfway rounds up.
Rounding to the Nearest Hundred and Thousand — one digit to the right decides.
Rounding to Estimate — know the size of the answer before the answer.
Rounding and Adjusting — add the round number, then give back the change (the exact-answer cousin).
Rounding Decimals to One and Two Decimal Places — the digit just after the cut decides.

Further up the ladder, Significant Figures and Estimating with Units carry the same ideas into their grown-up forms.

Start in the Counting & Place Value lessons and the Basic Arithmetic lessons in the app's Learn tab.

Practice it in the game

Two topics drill this guide directly. Rounding asks for the nearest ten, hundred and thousand (and decimals in hard mode). Estimation shows sums and products like ≈ 47 × 8 and asks for the honest ballpark — the wrong options are built to be half or double the truth, so recognizing the right SIZE is exactly the skill being trained.

Your turn

Three to try — tap what you get.

Roughly, 39 × 21 is closest to

Estimate 612 ÷ 29.

4.9 + 5.2 + 4.8 is closest to

Practice estimation free → Practice rounding free →