Video: Rounding the Area of a Rectangle given One of Its Side Lengths in Decimal Form

A rectangle has a length of 23.73 cm and a width of 10 cm. What is the area of the rectangle? Give your answer correct to the nearest square centimeter.

03:45

Video Transcript

A rectangle has a length of 23.73 centimetres and a width of 10 centimetres. What is the area of the rectangle? Give your answer correct to the nearest square centimetre.

The area of a 2D shape is the space inside it. And in this problem, we’re asked to give the area of the rectangle that we’re told about. So the area of the rectangle in the diagram is this space inside it. Now, to calculate the area of the rectangle, we need to know two pieces of information. Let’s remind ourselves what they are. The area of a rectangle is found by multiplying its length by its width. And if both the length and the width are in centimetres, then we measure the area of a rectangle in square centimetres. We write this as centimetres with a little two.

So the two pieces of information we need to know are our rectangle’s length and its width. And in the question, also in the diagram, we’re told both of these measurements. Our rectangle has a length of 23.73 centimetres and a width of 10 centimetres. So if we multiply 23.73 by 10, we can then find the area of our rectangle, which will be in square centimetres. Now, when we think of the place value of a number, each digit to the left of another digit is worth 10 times as much. So, for example, a digit in the tens place is worth 10 times as much as the same digit in the ones place.

So in other words, if we want to make the digits in 23.73 10 times larger, which is what we want to do when we multiply by 10, all those digits are going to have to do is to shift one place to the left. Two tens will become two hundreds. Three ones will now have a value of three tens or 30. Seven tenths will now become worth seven ones and three hundredths become three tenths. 23.73 multiplied by 10 equals 237.3. And so we can say that the area of our rectangle is 237.3 centimetres squared or square centimetres.

Notice, though, that we’re asked to give our answer correct to the nearest square centimetre, in other words, the nearest whole square centimetre. The number 237.3 is in between the whole numbers 237 and 238. Now, the midpoint between these two numbers is 237 and a half which we can write as a decimal as 237.5. We know that 237.3 is less than 237.5. It might be about here on our number line. And so we can say that if we round this to the nearest whole square centimetre, this is going to be 237.

If a rectangle has a length of 23.73 centimetres and a width of 10 centimetres, we can find the area of that rectangle by multiplying the two numbers together. We did this and then we rounded our answer to the nearest whole number. This gives the area of the rectangle as 237 centimetres squared or square centimetres.

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