42/100 as a Decimal, Fraction and Percent: All Three Forms Explained

Quick answer first, since it’s probably why you’re here: 42 100 as a decimal is 0.42.

If your homework only wants that number, you’re done. Most students get asked for the fraction and the percent as well though, and sooner or later a teacher wants to see the working. That’s what the rest of this page is for. It’s a small topic and a fairly friendly one, because the number 100 does most of the heavy lifting.

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What is fraction?

Take 42/100 apart. The bottom number says something has been cut into 100 equal pieces, and the top number says you’re holding 42 of them. Draw a ten by ten grid on graph paper and colour in 42 squares. That’s 42/100 of the grid. Nothing mysterious in it.

The reason hundreds are so easy is that decimals are built on tens. Anything over 10, 100 or 1000 is already a decimal wearing a fraction costume, and you only have to take the costume off.

How to Write 42/100 as a Decimal

The fraction bar means divide, so 42/100 is 42 ÷ 100. Forty two is smaller than a hundred, so you know the answer is under 1 before you even start. Write 42 as 42.00 and do long division. A hundred goes into 420 four times, that’s 400, leaving 20. Pull down the next zero to get 200, and a hundred goes into that twice. No remainder. The answer is 0.42.

I’ll be honest, almost nobody does long division for a hundred unless a teacher insists on it. There are quicker ways.

Where 0.42 Sits on a Number Line

The first is to read it out loud. 42/100 is forty two hundredths. The first place after the decimal point is tenths and the second is hundredths, so the 4 goes in the tenths spot and the 2 goes in the hundredths spot. That gives 0.42. If you want to check it, four tenths is the same as 40 hundredths, and two more hundredths takes you to 42.

The second is the one I’d use in an exam. Dividing by 100 slides the decimal point two places to the left. Write 42 as 42.0, slide the point twice, and there’s your 0.42. It works on 7/100 as well, but you need a zero to hold the place, so you get 0.07 and not 0.7. That’s where marks get dropped, by the way. Plenty of people see 7/100 and write 0.7 without thinking.

What if the top number is bigger than the bottom? Same rule. 142/100 becomes 1.42, because you’ve got more than one whole, which is exactly what the answer should look like.

If it helps to picture it, imagine a number line from 0 to 1. Halfway is 0.5, and 0.42 sits just before that, a little under halfway along.

Since 0.42 stops after two digits and doesn’t loop forever, it’s called a terminating decimal. You’ll see that phrase in textbooks, so it’s good to know what it means.

How to Simplify 42/100 as a Decimal and Fraction

42/100 is perfectly correct as it stands, but most teachers want it reduced. Both numbers are even, so cut them in half and you get 21/50. Can you go further? 21 is 3 times 7 and 50 is 2 times 5 times 5. Nothing in common, so no. 21/50 is as small as it gets.

Want proof it’s the same number? Type 21 ÷ 50 into a calculator and 0.42 pops out.

42/100 as a Percent: The Easiest Conversion

This is the easy one. Percent means per hundred, so 42 out of 100 is 42%. There’s no calculation at all. If you’re starting from the decimal, multiply by 100, so 0.42 × 100 = 42. Going back the other way, divide by 100. And if all you’ve got is 21/50, double both numbers to get 42/100 and you’re back on familiar ground.

Why Write 42/100 as a Decimal When You Already Have a Fraction?

Fair question. Each one suits a different job. Fractions are nice when you’re splitting something into equal portions, like 21 seats out of 50. Decimals are what calculators and money use. Percents are for comparing things, because everything gets measured out of the same hundred, which is why a shop sign says 42% off and doesn’t say 0.42 off. Examiners love percentages for the same reason, so expect to see this kind of conversion on tests again and again.

Where You See 42/100 as a Decimal Every Day (Discounts, Batteries, Marks and Money)

A shirt costs ₹500 and the shop takes 42% off. That’s 0.42 × 500 = ₹210, so you pay ₹290. A phone sitting on 42% battery is a bit under half charged, which is that annoying zone where you tell yourself you’ll be fine. Score 42 in a test out of 100 and that’s 42%, or 0.42 if your teacher prefers decimals. Forty two paise is ₹0.42, and forty two cents is $0.42, same logic. If 42 out of 100 people surveyed say they’d pick tea over coffee, you can call that 42%, 0.42, or 21 in every 50. All three are right.

3 Mistakes to Avoid When Converting

The commonest mistake is moving the decimal point the wrong number of times. Someone writes 4.2 or 0.042 and the working looks fine until you notice the point has moved once, or three times, instead of twice. A hundred has two zeros, so it’s two places.

Second is mixing up 0.42 and 0.42%. One tiny symbol and the value is completely different, since 0.42% works out to 0.0042.

Third, and this one is more common than you’d think, is believing 21/50 and 42/100 are different numbers. They’re the same amount. It’s like saying half instead of fifty percent.

A quick check saves you from most of this. 42 is a bit under half of 100, so your decimal should be a bit under 0.5 and your percent a bit under 50%. If you end up with 4.2 or 420%, go back and look again.

Conclusion

Try these in your notebook. Write 37/100 as a decimal and a percent. Turn 0.65 into a fraction in simplest form. Change 58% into a decimal and a fraction. Look away now if you don’t want the answers: 0.37 and 37%, then 13/20, then 0.58 and 29/50.

That’s really all there is to it. 0.42, 21/50 and 42% are one amount, and after you’ve converted a few of them you stop needing to work it out from scratch.

Frequently Asked Questions

What is 42/100 as a decimal?

It’s 0.42. Divide 42 by 100, or slide the decimal point two places to the left.

hat is 42/100 as a percentage?

42%. Percent means out of a hundred, so the top number of a fraction over 100 is the percent.

Can 42/100 be reduced?

Yes, to 21/50. Divide the top and bottom by 2. After that, 21 and 50 have no common factor other than 1, so it can’t go any lower.

Is 0.42 a terminating or a repeating decimal?

Terminating. It ends after two decimal places and nothing repeats.

How do I change any fraction with 100 as the denominator into a decimal?

Take the numerator and move its decimal point two places to the left, adding zeros if you run out of digits. So 63/100 becomes 0.63 and 9/100 becomes 0.09.