Decimal Place Values and Rounding

Front

True or false: Decimals are another way to write numbers that aren't whole. They include a point to separate the whole part from the part that's less than a whole.

Back

True

Answer explanation

Decimals are another way to write numbers that are not whole. They are used to represent numbers that fall between whole numbers. The decimal point is used to separate the whole part from the part that is less than a whole. The digits to the right of the decimal point represent fractions of one, with each place value indicating a specific fraction (e.g., tenths, hundredths, thousandths, etc.). So, when you see a number like 2.75, the 2 is the whole part, and the 0.75 represents seventy-five hundredths, which is less than a whole.

Front

Which digit is in the tenths-place in the number 3.648?

Back

6

Answer explanation

The tenths place is the first digit to the right of the decimal point. To identify the digit in the tenths place, you simply look at the digit immediately to the right of the decimal point. In the number 0.648, it is the digit 6.

Front

Value of the digit 9 in the number 0.579?

Back

0.009

Answer explanation

In the number 0.579, the digit 9 is located in the thousandths place. The place value of each digit to the right of the decimal point is as follows: The first digit to the right of the decimal point represents tenths, the second digit to the right of the decimal point represents hundredths, and the third digit to the right of the decimal point represents thousandths. So, the digit 9 in 0.579 represents 9 thousandths, which is equivalent to 0.009.

Front

Write the number 0.513 in expanded form.

Back

0.5 + 0.01 + 0.003

Answer explanation

To express the number 0.513 in expanded form, you need to break it down into its individual place values: 0.5 represents five-tenths (5/10), 0.01 represents one-hundredth (1/100), and 0.003 represents three-thousandths (3/1000). When you add these together, you get: 0.5 + 0.01 + 0.003 = 0.513. So, 0.5 + 0.01 + 0.003, represents the expanded form of the number 0.513.

Front

Which decimal is equal to 0.07? Options: 0.007, 0.070, 0.7, 0.700

Back

0.070

Answer explanation

0.07 can be expressed as 0.070. When you write 0.07 as 0.070, it means you have seven-hundredths (7/100) and zero thousandths (0/1000), so the last zero does not change the number’s value.

Front

True or false: Rounding decimals is not useful for getting approximate answers.

Back

False

Answer explanation

Rounding decimals simplifies numbers and helps in estimating answers more easily. It provides a quick way to get a rough idea of the result without dealing with all the decimal places. So, the statement "Rounding decimals is not useful for getting approximate answers" is false.

Front

Round 8.5 to the nearest whole number (ones place).

Back

9

Answer explanation

When rounding a number to the nearest ones place, you look at the digit to the right of the ones place, which is the tenths place. If that digit is 5 or more, you round up the ones place. If it's 4 or less, you keep the ones place as it is. In the given number 8.5, the digit to the right of the ones place (the tenths place) is 5, which is 5 or more. Therefore, you round up the ones place. The answer is 9 because you increase the ones place by 1. If the digit to the right of the ones place were 4 or less, you would have kept the ones place as 8.

Front

Samantha's depth gauge reads 0.73 meters. Round to the nearest tenths place.

Back

0.7

Answer explanation

When rounding a number to the nearest tenths place, you look at the digit to the right of the tenths place, which is the hundredths place. If that digit is 5 or more, you round up the tenths place. If it's 4 or less, you keep the tenths place as it is. In this case, the depth reading is 0.73 meters. The digit to the right of the tenths place (the hundredths place) is 3, which is 4 or less. Therefore, you keep the tenths place as it is. The answer is 0.7 meters because you do not change the tenths place. If the digit to the right of the tenths place were 5 or more, you would have rounded up to 0.8 meters.

Front

Round 2.869 to the nearest hundredths place.

Back

2.87

Answer explanation

When rounding a number to the nearest hundredths place, you look at the digit to the right of the hundredths place, which is the thousandths place. If that digit is 5 or more, you round up the hundredths place. If it's 4 or less, you keep the hundredths place as it is. In the given number 2.869, the digit to the right of the hundredths place (the thousandths place) is 9, which is 5 or more. Therefore, you round up the hundredths place. The answer is 2.87 because you increase the hundredths place by 1. If the digit to the right of the hundredths place were 4 or less, you would have kept the hundredths place as 2.86.

Front

Round 0.1254 grams to the nearest thousandths place.

Back

0.125

Answer explanation

When rounding a number to the nearest thousandths place, you look at the digit to the right of the thousandths place, which is the ten-thousandths place. If that digit is 5 or more, you round up the thousandths place. If it's 4 or less, you keep the thousandths place as it is. In this case, the mass of the substance is 0.1254 grams. The digit to the right of the thousandths place (the ten-thousandths place) is 4, which is 4 or less. Therefore, you keep the thousandths place as it is. The answer is 0.125 grams because you do not change the thousandths place. If the digit to the right of the thousandths place were 5 or more, you would have rounded up to 0.126 grams.