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Chapter 2: Problem 41

Write the number in standard form. four hundred seven and three hundredths

Short Answer

Expert verified
The number four hundred seven and three hundredths written in standard form is 407.03.

Step by step solution

01

Identify the Whole Number

Identify the whole number from the given wording which is 'four hundred seven'. This can be written in standard form as '407'.
02

Identify the Decimal Number

Identify the decimal number which is 'three hundredths'. This is written in standard form as '0.03'.
03

Combine the Whole and Decimal Number

Combine the whole number and the decimal number to write the number in standard form. This gives us '407.03' as the number in standard form.

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Key Concepts

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

Understanding Decimal Numbers
Decimal numbers are numbers that include a whole number part and a fractional part separated by a decimal point. The fractional part is a fraction whose denominator is a power of ten. This makes decimal numbers easy to work with in arithmetic and everyday usage.
When you see a number like \(0.03\), the whole number part is zero, and the fractional part is '03'. Each digit to the right of the decimal point represents a power of ten. Here:
  • The '0' represents zero tenths
  • The '3' represents three hundredths
Understanding decimal numbers helps in accurately interpreting and writing numbers in standard form. It鈥檚 useful to think of decimal numbers as an expansion of place value into fractions.
Defining Whole Numbers
Whole numbers are simple numbers without any fractional or decimal part. They include all the natural numbers starting from zero: 0, 1, 2, 3, and so on. Whole numbers can be positive, including zero, but not negative.
In the standard form exercise, the whole number '407' is derived from the phrase 'four hundred seven'. Here,
  • '4' stands for four hundreds.
  • '0' stands for zero tens.
  • '7' stands for seven ones.
Understanding whole numbers is crucial because they form the core part of larger decimal numbers and are often used in conjunction with decimal fractions to express exact values in standard form.
Exploring Place Value
Place value is a fundamental concept in mathematics that defines the value of a digit based on its position within a number. Numbers are composed of different place values which can greatly alter their overall value.
In a number such as '407.03':
  • '4' is in the hundreds place, giving it a value of 400.
  • '0' in the tens place gives it a value of 0 because there are zero tens.
  • '7' in the ones place adds a value of 7.
  • After the decimal, '0' is in the tenths place, still contributing 0 to the total.
  • '3' in the hundredths place contributes \(0.03\) to the total value.
Correctly understanding place value is essential for interpreting numbers and especially important when writing numbers in standard form.
Navigating Number Representation
Number representation refers to the different ways a number can be expressed or written. Standard form is one of these methods, which combines whole numbers and decimal numbers into one clear and concise format.
Here are some elements involved in number representation:
  • Writing numbers in words: This can sometimes lead to long descriptions such as 'four hundred seven and three hundredths'.
  • Standard form: This is a shorter and more common mathematical representation such as '407.03'.
This representation aids in simplifying complex numbers and makes them easier to work with in calculations and comparisons. Knowing how to correctly translate written numbers to standard form is a practical skill in everyday mathematics.

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