All the solutions provided in McGraw Hill My Math Grade 5 Answer Key PDF Chapter 1 Review will give you a clear idea of the concepts.

Review

Vocabulãry Check

choose the correct word(s) to complete each sentence.

decimal decimal point equivalent decimals expanded form
period place value place-value chart standard form

Question 1.
Decimals that have the same value are ____.
Definition: When two decimals are representing the same fraction, they are called the decimal equivalent. In other words, equivalent decimals are decimals that are equal. Hence they are also called equal decimals.

Question 2.
____ is a system for writing numbers. In this system, the position of a digit determines its value.
Definition: Place value describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.

Question 3.
The usual or common way to write a number is called _____
A standard form of a number is basically mentioned for the representation of large numbers or small numbers. We use exponents to represent such numbers in standard form.

Question 4.
The way of writing a number as the sum of the values of its digits is called ___.
The expanded form of the numbers helps to determine the place value of each digit in the given number. It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form. For example, the expanded form of the number 1682 is 1000+600+80+2.

Question 5.
A ____ is a number that has a digit in the tenth place, hundredth place, and/or beyond.
decimals are one the types of numbers, which has a whole number and the fractional part separated by a decimal point.

Question 6.
The ____ is a period separating the ones and the tenths in a decimal number.
The dot present between the whole number and fractions part is called the decimal point. For example, 34.5 is a decimal number.

Question 7.
A ____ is a chart that shows the value of the digits in a number.
Place value charts help us to make sure that the digits are aligned in the correct places. A place value chart displays the correct position or place of a digit in a number. To identify the positional values or worth of different digits in a number accurately, we first write the given digits in the place value chart to check their position. In order to make the process easier, the larger numbers are divided into periods that are separated with the help of commas.

Concept Check

Name the place of the underlined digit. Then write the value of the digit.

Question 8.
195,489
Place value describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.

The underlined number is 5
5 is in the thousand’s place.

Question 9.
6,720,341
Place value describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one’s position. The order of place value of digits of a number of right to left is units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.

The underlined number is 6
6 is in the hundred thousand places.

Write each number in standard form.

Question 10.
94 million, 237 thousand, 108 ____
A Standard Form is a process of formulating a given mathematical concept such as a number, equation, polynomial, etc. in the standard form by following certain basic rules.
Standard Form of a Number:
The definition of the standard form of a number is representing the very large expanded number in a small number.
The standard form of a number is 94,237,108

Question 11.
8 × 1,000,000 + 5 × 10,000 + 2 × 1,000 + 6 × 100 ____
8,000,000 + 50,000 + 2,000 + 600
Place value charts help us to make sure that the digits are aligned in the correct places. A place value chart displays the correct position or place of a digit in a number. To identify the positional values or worth of different digits in a number accurately, we first write the given digits in the place value chart to check their position. In order to make the process easier, the larger numbers are divided into periods that are separated with the help of commas.

In standard form, we can write as 8,052,600

Shade the model to show each fraction. Write each fraction as a decimal.

Question 12.
$$\frac{19}{100}$$

The above-given model is the hundredth cube.
In fractions, we can write as 19/100
In decimals, we can write it as 0.19

Question 13.
$$\frac{8}{10}$$

The above-given model is the tenth cube
In fractions, we can write as 8/10
In decimals, we can write it as 0.8

Write each number ¡n standard form and expanded form.

Question 14.
five and nine tenths
The expanded form of the numbers helps to determine the place value of each digit in the given number. It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form.
(5 x 1) + (9 x 1/10)
Standard form:
5.90
5 is in the one’s place
‘.’ represents “and”
9 is in the tenth place.

Question 15.
seven hundred twelve thousandths
The expanded form of the numbers helps to determine the place value of each digit in the given number. It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form.
(0 x 100) + (7 x 1/10) + (1 x 1/100) + (2 x 1/1000)
The standard form is 0.712

Write <, >, or = in each to make a true sentence.

Question 16.
14,589  14,985
Explanation:
There are certain rules, based on which it becomes easier to compare numbers. These rules are:
– Numbers with more digits
– Numbers starting with a larger digit
Since, both the numbers, 14589 and 14985 are having five digits thus we will compare the left-most digit of both numbers.
– As we can see the first two digits are the same for both numbers, thus we need to compare the next left-most digit of both numbers.
5 < 9
Therefore, 14,589 < 14,985
Hence, 14,589 is less than 14,985

Question 17.
506,789  505,789
Explanation:
Since, both the numbers, 506,789 and 505,789 are having six digits thus we will compare the left-most digit of both numbers.
– As we can see the first two digits are the same for both numbers, thus we need to compare the next left-most digit of both numbers.
6 > 5
Therefore, 506,789 > 505,789
Hence, 506,789 is greater than 505,789

Question 18.
8,913  8,931
Explanation:
Since, both the numbers, 8,913 and 8,931 are having four digits thus we will compare the left-most digit of both numbers.
– As we can see the first two digits are the same for both numbers, thus we need to compare the next left-most digit of both numbers.
1 < 3
Therefore, 8,913 < 8,931
Hence, 8,913 is less than 8,931

Question 19.
0.49  0.71
Explanation:
Since, both the numbers, 0.49 and 0.71 are having three digits thus we will compare the left-most digit of both numbers.
– As we can see the first digit is the same for both numbers, thus we need to compare the next left-most digit of both numbers.
4 < 7
Therefore, 0.49 < 0.71
Hence, 0.49 is less than 0.71

Question 20.
9.02  9.020
Explanation:
They both are equivalent decimals. Because all the place values of digits are the same.
If we put ‘0’ in the thousandth place then the first number becomes 9.020
or else 9.020 is nothing but 9.02
Finally, we can write as 9.02 is equal to 9.020
9.02 = 9.020

Question 21.
0.843  0.846
Explanation:
Since, both the numbers, 0.843 and 0.846 are having four digits thus we will compare the left-most digit of both numbers.
– As we can see the first three digits are the same for both numbers, thus we need to compare the next left-most digit of both numbers.
3 < 6
Therefore, 0.843 < 0.846
Hence, 0.843 is less than 0.846

Question 22.
Order the set of numbers from least to greatest.
13.84, 13.097, 12.655, 13.6
Ascending order is a method of arranging numbers from smallest value to largest value. The order goes from left to right. It is also named increasing order.
The above-given numbers: 13.84, 13.097, 12.655, 13.6
compare the numbers, after sorting out the numbers, the answer is:
12.655, 13.097, 13.6, 13.84

Problem Solving

Question 23.
One cup is equal to $$\frac{5}{10}$$ pint. Write this fraction as a decimal.
The above-given fraction is 5/10
We have to write in decimal form.
The decimal form can write as 0.5

Question 24.
Charles is moving from Springfield, which has 482,653 people, to Greenville, which has 362,987 people. Is he moving to a city with a greater or smaller population? Explain.
The number of people in Springfield = 482,653
The number of people in Greenville = 362,987
Now we have to find out whether Charles is moving to a city with the greatest population or a smaller population.
Now compare the numbers.
Charles is moving to Greenville.
both are having the same number of digits. So compare the left-most digit.
3 < 4
Therefore, 362,987 is less than 482,653
Hence, Charles is moving to a city with a smaller population.

Question 25.
The Pacific Ocean has sixty-four million, one hundred eighty-six thousand, three hundred square miles. How many square miles is the Pacific Ocean in standard form?
A Standard Form is a process of formulating a given mathematical concept such as a number, equation, polynomial, etc. in the standard form by following certain basic rules.
Standard Form of a Number:
The definition of the standard form of a number is representing the very large expanded number in a small number.
In the standard form, we can write a 64,186,300
Therefore, the square miles is the pacific ocean is 64,186,300 miles.

Test Practice

Question 26.
Which number results in a true sentence in 475 < ___?
A. 473
B. 474
C. 475
D. 476
You can go for option verification.
Check option D holding with number 476.
Compare 475 and 476
The first two digits are the same. So compare the next left-most digit.
5 < 6
Therefore, 475 < 476.

Reflect

Use what you learned about place value to complete the graphic organizer.