Year 5 Maths Homework: How to Understand and Use Place Value
Year 5 Maths Homework Place Value: How to Understand and Use Large Numbers
Place value is one of the most important concepts in maths. It helps us to read, write, compare, and round large numbers. In Year 5, you will be learning about place value up to 1,000,000 (one million). You will also learn about negative numbers, decimals, and Roman numerals. In this article, we will explain what place value is and how to use it in different situations.
Year 5 Maths Homework Place Value
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What is place value?
Place value is the value of each digit in a number based on its position. For example, in the number 123,456, the digit 1 is in the hundred thousands place, so it has a value of 100,000. The digit 2 is in the ten thousands place, so it has a value of 10,000. The digit 3 is in the thousands place, so it has a value of 1,000. The digit 4 is in the hundreds place, so it has a value of 100. The digit 5 is in the tens place, so it has a value of 10. The digit 6 is in the ones place, so it has a value of 1.
We can use a place value chart to show the value of each digit in a number. Here is a place value chart for numbers up to 1,000,000:
Hundred thousandsTen thousandsThousandsHundredsTensOnes
100,00010,0001,000100101
123456
We can also use commas to separate each group of three digits in a large number. This makes it easier to read and write large numbers. For example, we write 123,456 instead of 123456.
How to read and write large numbers?
To read and write large numbers, we need to know the names of each group of three digits. Here are the names of some common groups:
A group of three digits in the ones place is called a unit. For example, 456 is four hundred and fifty-six units.
A group of three digits in the thousands place is called a thousand. For example, 123,000 is one hundred and twenty-three thousand.
A group of three digits in the millions place is called a million. For example, 456,000,000 is four hundred and fifty-six million.
A group of three digits in the billions place is called a billion. For example, 123,456,000,000 is one hundred and twenty-three billion four hundred and fifty-six million.
A group of three digits in the trillions place is called a trillion. For example, 456,000,000,000,000 is four hundred and fifty-six trillion.
To read a large number, we start from the left and read each group of three digits followed by its name. We use the word and before the last group of digits. For example:
123 is one hundred and twenty-three.
12,345 is twelve thousand three hundred and forty-five.
123,456 is one hundred and twenty-three thousand four hundred and fifty-six.
1,234,567 is one million two hundred and thirty-four thousand five hundred and sixty-seven.
12,345,678 is twelve million three hundred and forty-five thousand six hundred and seventy-eight.
123,456,789 is one hundred and twenty-three million four hundred and fifty-six thousand seven hundred and eighty-nine.
1,234,567,890 is one billion two hundred and thirty-four million five hundred and sixty-seven thousand eight hundred and ninety.
12,345
How to compare and order large numbers?
To compare and order large numbers, we need to look at the value of each digit in each number. We can use a place value chart to help us. Here are some steps to follow:
Start by comparing the digits in the highest place value. For example, if we want to compare 123,456 and 234,567, we start by comparing the digits in the hundred thousands place: 1 and 2.
The larger digit means the larger number. For example, 2 is larger than 1, so 234,567 is larger than 123,456.
If the digits in the highest place value are equal, move to the next place value and compare the digits there. For example, if we want to compare 123,456 and 124,567, we start by comparing the digits in the hundred thousands place: 1 and 1. They are equal, so we move to the ten thousands place and compare the digits there: 2 and 4.
Repeat this process until you find a pair of digits that are different or you reach the ones place. For example, if we want to compare 123,456 and 123,789, we start by comparing the digits in the hundred thousands place: 1 and 1. They are equal, so we move to the ten thousands place and compare the digits there: 2 and 2. They are equal, so we move to the thousands place and compare the digits there: 3 and 3. They are equal, so we move to the hundreds place and compare the digits there: 4 and 7.
The smaller digit means the smaller number. For example, 4 is smaller than 7, so 123,456 is smaller than 123,789.
We can use symbols to show how two numbers are related. The symbols are:
< means less than. For example, 123 < 456 means 123 is less than 456.
> means greater than. For example, 789 > 456 means 789 is greater than 456.
= means equal to. For example, 123 = 123 means 123 is equal to 123.
To order a set of numbers from smallest to largest or from largest to smallest, we can use the same method of comparing digits in each place value. For example:
To order these numbers from smallest to largest: 12,345, 23,456, 34,567, 45,678, we start by comparing the digits in the ten thousands place: 1, 2, 3, 4. The smallest digit is 1, so 12,345 is the smallest number. The next smallest digit is 2, so 23,456 is the next smallest number. The next smallest digit is 3, so 34,567 is the next smallest number. The largest digit is 4, so 45,678 is the largest number. The order from smallest to largest is: 12,345 < 23,456 < 34,567 < 45,678.
To order these numbers from largest to smallest: 56,789, 67,890, 78
How to round large numbers?
Rounding is a way of simplifying numbers by making them close to a certain value. Rounding can help us to estimate and check our answers. To round a number, we need to decide which place value we want to round to. For example, we can round to the nearest 10, 100, 1,000, 10,000, or 100,000. Here are some steps to follow:
Identify the digit in the place value you want to round to. For example, if we want to round 123,456 to the nearest 10,000, we look at the digit in the ten thousands place: 2.
Look at the digit to the right of that digit. For example, if we want to round 123,456 to the nearest 10,000, we look at the digit to the right of 2: 3.
If the digit is 5 or more, increase the digit in the place value you want to round to by 1. If the digit is 4 or less, keep the digit in the place value you want to round to as it is. For example, if we want to round 123,456 to the nearest 10,000, we look at the digit 3. It is less than 5, so we keep the digit 2 as it is.
Replace all the digits after the digit in the place value you want to round to with zeros. For example, if we want to round 123,456 to the nearest 10,000, we replace all the digits after 2 with zeros: 120,000.
We can use a number line to help us visualise rounding. For example:
The number line shows that 123456 is closer to 120000 than to 130000 on the number line. So we round it down to 120000.
How to use negative numbers?
Negative numbers are numbers that are less than zero. They have a minus sign (-) in front of them. For example: -1, -2, -3, -4, -5, etc. Negative numbers are used in many situations, such as temperature, height below sea level, debt, and loss. For example:
The temperature in Antarctica can be as low as -60C.
The Dead Sea is about -430 m below sea level.
If you owe someone 10, you have a debt of -10.
If you lose 5 in a game, you have a loss of -5.
We can use a number line to show negative numbers. Negative numbers are on the left of zero and positive numbers are on the right of zero. The further away from zero a number is, the larger its value is. For example:
The number line shows that -3 is less than -2 and -2 is less than -1. It also shows that -1 is less than 0 and 0 is less than 1.
How to use decimals?
Decimals are a way of writing numbers that are not whole. Decimals have a decimal point (.) that separates the whole part and the fractional part of the number. For example, 3.14 is a decimal number that has 3 as the whole part and 14 as the fractional part.
We can use a place value chart to show the value of each digit in a decimal number. Here is a place value chart for numbers up to 1,000 with decimals:
HundredsTensOnes.TenthsHundredthsThousandths
100101.0.10.010.001
304.567
The number 3.14 has 3 in the ones place and 14 in the fractional part. The fractional part has 1 in the tenths place and 4 in the hundredths place. This means that 3.14 is equal to 3 + 0.1 + 0.04.
We can use decimals to show parts of a whole, such as fractions or percentages. For example:
A half can be written as 0.5 or 50%.
A quarter can be written as 0.25 or 25%.
A tenth can be written as 0.1 or 10%.
A hundredth can be written as 0.01 or 1%.
A thousandth can be written as 0.001 or 0.1%.
We can also use decimals to show measurements that are not exact, such as length, weight, or time. For example:
The length of a pencil can be measured as 15.3 cm.
The weight of an apple can be measured as 0.12 kg.
The time of a race can be measured as 12.45 seconds.
Conclusion
Place value is a key concept in maths that helps us to read, write, compare, and round large numbers. In Year 5, you will be learning about place value up to 1,000,000 and how to use negative numbers, decimals, and Roman numerals. You will also learn how to apply place value skills to different situations, such as temperature, height, debt, loss, fractions, percentages, and measurements. Place value can help you to estimate and check your answers and to make sense of the world around you.
We hope you found this article helpful and that you enjoy learning about place value in Year 5. If you want to practice your place value skills, you can find some worksheets and games on the links below. Have fun with maths! b99f773239
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