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Rounding numbers using the place value number system










































Rounding to the nearest hundredth

Using the place value system (base 10), round 46.605 seconds to the nearest hundredth of a second.

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Aug 29, 2012
Rounding to the nearest hundredth
by: Staff


Answer:


Part I

First, let’s review what the place value system is.

Our modern number system uses a number base of ten with place-value notation.

Its official name is the International Place-Value Number System.

The place value system we use is practical and efficient when compared to other number systems such as the ancient Roman or Egyptian systems. It is easy to use because there are only 10 symbols to memorize: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. There is no need to memorize any other symbols for ordinary arithmetic. These 10 digits can be used over and over again to write any number.

In a place-value number system, the magnitude of the number depends upon two things: (1) the face value of the digit used (0, 1, 2, 3, 4, 5, 6, 7, 8, or 9), and (2) the POSITION of the digit in the number.

Place-value notation uses same symbol for over and over again to stand for different orders of magnitude.

For example, the number digit “5” is used for 5, 50, 500, 5000, and so on.

In the United States, we often use a comma as a separator to group digits together.

Each group of 3 digits is called a period. Each period has a different name.

Here is an example of a large number which uses a comma as a separator: 987,654,321,098,765

The names of the periods are:

987 – Trillion
654 – Billion
321 – Million
098 – Thousand
765 – Ones

Although we don’t group decimals using a separator, the position of each decimal digit does have a name.


For example: 0.123456

The position of every digit has a name:

1 – tenth
2 – hundredth
3 – thousandth
4 – ten-thousandth
5 – hundred-thousandth
6 – millionth

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Aug 29, 2012
Rounding to the nearest hundredth
by: Staff


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Part II


Mathematically, the following number can be divided into parts based on the magnitude of each of the numbers according to their position in the number:

123.456

= 100 + 20 + 3 + .1 + .05 + .006

Because our number base is 10, each of these digits can be written as a multiple of 10:

= 1*10² + 2*10¹ + 3*10⁰ + 1*10⁻¹ + 5*10⁻² + 6*10⁻³


Now for your specific question on rounding:

Round 46.605 seconds to the nearest hundredth of a second.

When rounding to the nearest hundredth, you are rounding to this digit:

46.605

Now look to the right of the hundredths digit.

46.605


If the number to the right of the hundredths digit is 0, 1, 2, 3, or 4, then drop all the numbers to the right of the hundredths digit. Do not change the value of the hundredths digit.

If the number to the right of the hundredths digit is 5, 6, 7, 8, or 9, then round up the value of the hundredths digit and drop all the numbers to the right of the new hundredths digit.


Since the number immediately to the right of the hundredths digit (shown in red) is 5, then round up the value of the hundredths digit and drop all the numbers to the right of the new hundredths digit.



Final Answer


46.605 seconds rounded to the nearest hundredth of a second = 46.61.




Thanks for writing.

Staff
www.solving-math-problems.com


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