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Chapter 1: Problem 94

Round the number to the given place value. $$36,702,599 ; \text { millions }$$

Short Answer

Expert verified
The number \(36,702,599\) rounded to the nearest million is \(37,000,000\).

Step by step solution

01

Identify the Place Value

Identify the place value to which the number has to be rounded off. In this case, it is the millions place. The number is \(36,702,599\). So, the millions digit is '6'.
02

Check the Digit Right to the Place Value

Check the digit on the right of the identified place. If it's less than 5, the digit in the identified place will remain unchanged. If it's 5 or more, add 1 to the digit in the identified place. In this case, the right digit is 7 which is greater than 5.
03

Implement Rounding

Since the digit right to the millions place is more than five, add 1 to the digit in the millions place and replace all the digits on the right of millions place by zeros. So, the million digit '6' will become '7' and all other digits should be replaced by zeros.
04

Display the Result

The rounded off value is \(37,000,000\). This is the closest million to the given number \(36,702,599\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Place Value
Understanding place value is fundamental to rounding numbers effectively. In essence, place value tells us the worth of a digit based on its position in a number.

For instance, in the number 36,702,599, each digit is part of a larger system. The digit '3' stands in the ten million place, while '6' occupies the millions place.
Digits further right reduce in place value from hundreds of thousands, down to units. Recognizing this helps us quickly identify which digit to look at when rounding a number to a specific place value.
Rounding to Millions
Rounding to millions means adjusting a number so that it is a simpler, approximate value closest to the original number, but focusing on the millions place.

Let's take the number 36,702,599 as an example. The digit in the millions place is '6'.
When we round to the nearest million, we're determining if this '6' stays '6' or rounds up to '7'.
Once rounding is complete, digits to the right become zeros, simplifying the number to a cleaner form. Hence, 36,702,599 would round to 37,000,000 when rounded to the nearest million.
Essential Number Rounding Rules
Number rounding rules are a set of guidelines that help you decide how to adjust a number to make it cleaner and easier to work with. Here are the basic steps:
  • Identify the digit at the place value you're rounding to. This tells you which digit will potentially change.
  • Look at the digit immediately to the right of your chosen place value. This "neighboring digit" determines your next move.
  • If this neighboring digit is 5 or more, you increase the place value digit by one.
  • If this neighboring digit is less than 5, you leave the place value digit as it is.
  • All digits to the right of the rounded place become zeros, simplifying the number dramatically.
Applying these rules, as in our example, ensures accuracy and makes large numbers much easier to handle.

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