Learning to count whole numbers is fun and easy. However, once you realize that a period could be a decimal point and that adding zeros may not matter at all or may matter a whole lot, math gets a lot trickier.
0.2 is greater than 0.02 in the decimal system. To the left of the decimal point, the more zeros that are between the decimal and the numeral, the greater the number. However, to the right of the decimal, the more zeros that are between the decimal and the digit, the smaller the number.
So, what if we throw even more zeros in there? Or what if we take them out?
Is 0.2 Or 0.02 Higher?
0.2 is higher than 0.02 numerically. For decimal numbers to the right of the decimal point, numbers closer to the decimal are higher than those further from the decimal. An excellent way to check your understanding is to count money.
We base decimal numbers on increments of 10 for the number immediately preceding it (source). So, 0.2 is 2/10ths of 1 while 0.02 is 2/10ths of 0.1 or 1/50th (2/100 simplified) of 1.
In other words, decimal numbers (right of the decimal) grow larger from right to left. For example, it takes 10 thousandths (0.001) to make 1 hundredth (0.01) and 10 hundredths to make 1 10th (0.1). Likewise, ten tenths make one whole number (1.0).
An easy way to think of which one is higher is to count money. If we use the U.S. dollar system, then $1 would be either 10 dimes or 100 pennies. Decimally, one dime is $0.10, and one penny is $0.01. Which one is higher?
You need 10 dimes to make $1 and 10 pennies to make $0.10. Further, you need 100 pennies to make $1. This is the decimal system in practice!
To go one more decimal place beyond the hundredth is the thousandths place (0.001). The American dollar system does not have a monetary unit in this placeholder as it would be measuring tenths of a penny.
Which Is Bigger .2 or .02?
.2 is bigger than .02. Taking the whole number — left of the decimal point — off of the number does not impact whether .2 or .02 is greater because placement closer to the decimal determines decimal size on the left.
Continuing with our money example in the previous section, are two dimes ($0.20) or two pennies ($0.02) worth more? Two dimes, of course!
Whatever dollar amount (whole number) is on the left side of the decimal does not change the fact that the sum of two dimes ($0.20) is greater than two pennies ($0.02). However, whichever dollar amount is greater on that left side determines which number is greater overall.
For example, is $1.20 more than $3.02? Nope! Though the decimal number 0.20 is greater than 0.02, $3 is still greater than $1.
- $3.02 is bigger than $1.20.
- $2.01 is bigger than $2.00.
But, if both whole numbers (dollar amounts) are equal or nonexistent, then we determine size by which decimal number closest to the decimal place is greater.
- 1.2 or 1.02? 1.2 is bigger.
- 0.2 or 0.02? 0.2 is bigger.
- .2 or .02? .2 is bigger.
Should I Add a Zero?
To avoid confusion, it is best to always put something on the left side of the decimal place (whole number). If there is no whole number value, place a zero there: 0.2. In this way, someone is less likely to overlook the decimal point.
A zero is only necessary on the right-hand side of the decimal place if there is no numerical value in the decimal place closer to the decimal.
You cannot simplify 0.000004 to 0.4 because 0.4 is much bigger than 0.000004. Those zeros help the reader understand that 0.000004 is four-millionths of one. Taking out any of those zeros will alter the value of the number.
On the other hand, adding zeros after a decimal number does not add any meaning to the value whatsoever.
- 0.0300 = 0.03
- 1.2750 = 1.275
You may see unnecessary zeros in currency notation to the hundredths or thousandths place — depending on the currency noted — to standardize decimal currency notation. For example, the American currency system notates to the hundredth place because the American dollar is made up of 100 pennies.
- $1.75
- $5.30
You should not add zeros to the left side of the whole number, either. Additional zeros only add value if holding a place closer to the decimal point.
- 010.01 = 10.01
- 065.60 = 65.6
So, avoid adding zeros to the far right or left of a number and do not remove any zeros between the numerals.
The Decimal System
The decimal system is a counting or measurement system based on powers of 10. Each decimal place on either side of the decimal point can span from 0 to 9 (source). The value of each number increases from right to left, with the digit furthest to the right being the smallest.
On the left-hand side of the decimal point are whole numbers. A whole number is not divided into pieces; 100% of the number stands to the left of a decimal point.
- 5.0 means five whole numbers
- 2 means two whole numbers
- $4.56 means four whole dollars and 0.56 of another dollar
The decimal places on the right-hand side of the decimal point are decimal numbers. Decimal numbers are not whole. Instead, they are tenths, hundredths, thousandths, and so on of one. We can also note these as fractions.
- 0.1 = one tenth or 1/10
- 0.01 = one hundredth or 1/100
- 0.001 = one thousandth or 1/1000
For more on understanding the size of decimal numbers, check out our article “Which is Greater: 0.1 or 1.0?”
How do you make a decimal into a fraction?
Fraction or Decimal?
We can note a decimal number fractionally by putting the decimal number over the decimal place it represents.
- 0.5 is five tenths or 5/10
- 0.02 is two hundredths or 2/100
However, these two examples are not complete. We must simplify a fraction by the highest number we can equally divide the top and bottom by until we can divide neither number by anything more than one. This keeps the fractions clean and easy to read.
Let’s simplify the examples above:
- 0.5 = 5/10. We can divide both 5 and 10 by 5, so we do so to get 1/2.
- 0.02 = 2/100. We can divide both 2 and 100 by 2 until we get 1/50.
Fraction simplification is why fractions and their decimal notations look different.
- 0.75 = 75/100 = 3/4
- 0.250 = 250/1000 = ¼
Obviously, fractions can be a bit tricky. But, if fractions take additional steps to make and simplify, why do we use them at all?
Should I Use a Fraction or a Decimal Number?
Whether you use a fraction or a decimal number is up to you. However, most prefer the decimal system for counting currencies and for measurement. In fact, the Metric System is based entirely on the decimal system (source).
Many recognize the decimal system as more exact because it does not require additional simplification steps. If 0.0376 is not accurate enough, simply add another decimal place.
Verbally, however, it is more comfortable to say “half an inch” (1/2 inch) than to say “zero point five inches” or “five-tenths of an inch” (0.5 inch). You are also more likely to say, “Joe ate one and a half pizzas last night,” rather than, “Joe ate one point five pizzas last night.”
Conversely, people are more likely to remember pi (π) as 3.1415 than 22/7. It certainly seems that the more complicated the number — i.e., the more decimal places after the decimal point — then the more likely a person is to verbally say the decimal value over the fraction.
This article was written for strategiesforparents.com.
Writing, though, is much more equalized between the two numerical notations. Some may argue that writing decimally is cleaner and easier to see, but plenty of people still prefer writing fractionally. So the choice comes down to a specific style or personal preference in writing.
Final Thoughts
0.2 is greater than 0.02 because 2/10ths is greater than 2/100ths. The easiest way to picture this is to think of counting currency. In the U.S. currency system, $0.20 is worth more than $0.02. We can also note decimal numbers fractionally.
The next time you measure something or count change, think of how you can express the amount you are looking at fractionally or decimally. Which method did you choose and why?