Numbers 10000

Place value tells us how much a digit is worth depending on its place. In numbers up to 10,000 we use four main places: units, tens, hundreds and thousands. Each place stands for a value ten times the place to its right. For example, in the number 3 5 2 7 the digit 3 is in the thousands place and means 3000, 5 in the hundreds place means 500, 2 in the tens place means 20 and 7 in units means 7.

We write the places from right to left as units, tens, hundreds, thousands. A digit in the thousands place can be 1 to 9 for numbers less than 10,000. Knowing place value helps us to compare numbers, add and subtract correctly, and break numbers into parts for easier calculation.

We must also learn to use commas or spaces to group digits in threes from the right, for example 3,527 or 3527. This helps to read larger numbers quickly and avoid mistakes.

Reading numbers means saying them in words clearly and correctly. Writing numbers means showing them as digits (figures) or writing the words that name them. For numbers up to 10,000 the usual order is to say the thousands part first, then the hundreds part, and finally the tens and units. For example, 2,345 is read as 'two thousand three hundred forty five'. At this class level, it is best to avoid extra words like 'and' when reading numbers aloud; say the parts in sequence so the meaning stays clear.

When a place has zero, we skip that place-word. For instance, 3,045 is read as 'three thousand forty five' because there are no hundreds. Similarly 7,008 becomes 'seven thousand eight' not 'seven thousand zero hundred eight'. Learn the spellings for tens words: twenty, thirty, forty, fifty, sixty, seventy, eighty, ninety; these are used with unit words (e.g., twenty three).

Writing numbers from words follows the reverse steps: identify the thousands part, write its digit(s), then the hundreds, then the tens and units. Check carefully for zeros and correct place value. Practise both conversions regularly—words to figures and figures to words—to avoid common errors. Clear reading and writing of numbers are useful when dealing with money, time, measurements and classroom tests.

Expanded form shows a number as a sum of each digit multiplied by its place value. For a number like 5,432 we write 5000 + 400 + 30 + 2. This breaks the number into parts so we can see how it is built. Standard form (or short form) is the usual way of writing the number as digits, like 5,432.

Expanded form is useful when adding or subtracting because we can work with each place separately. It is also helpful to check the value of each digit. You can also write expanded form using multiplication: 5 × 1000 + 4 × 100 + 3 × 10 + 2 × 1.

To convert from expanded to standard form, add the parts together. To convert from standard to expanded, write each digit times its place value. Practice with zeros: 7,205 = 7000 + 200 + 0 + 5; you may omit adding 0 in the sum when writing neatly.

Comparing numbers means deciding which number is larger, smaller, or if they are equal. For numbers up to 10,000, the easiest way is to compare digits from left (the highest place) to right. First look at the thousands place: the number with the bigger thousands digit is larger. If the thousands digits are the same, compare the hundreds digits next; if those are the same, compare tens; if tens are the same, compare units. Follow this step-by-step method every time to avoid mistakes.

Use the symbols '>' (greater than), '<' (less than) and '=' (equal to) to show the result. For example, to compare 3,421 and 3,412 we see both have 3 in thousands and 4 in hundreds; tens differ (2 versus 1), so 3,421 > 3,412. When numbers have different total digits, like 4,321 and 321, the one with more digits (4,321) is larger because it has a non-zero thousands digit.

Ordering numbers means arranging them from smallest to largest (ascending) or largest to smallest (descending). A helpful method is to write all numbers one beneath another with their digits lined up by place value, then read across the columns to place each number. Also practise using number lines to visualise ordering. Comparing and ordering are used in day-to-day life for scores, prices and measurements, so practising many examples strengthens speed and accuracy.

The successor of a number is the number that comes immediately after it when counting; you get it by adding one. The predecessor is the number that comes immediately before; you get it by subtracting one. When adding or subtracting one, watch for carrying and borrowing across places. For example, the successor of 2,999 is 3,000 because adding one to 2,999 causes all digits to roll over. Similarly, the predecessor of 3,000 is 2,999 because subtracting one borrows through the zeroes.

Even and odd numbers are determined by the units digit. An even number ends in 0, 2, 4, 6 or 8 and can be divided exactly by 2. An odd number ends in 1, 3, 5, 7 or 9 and leaves a remainder of 1 when divided by 2. For any number up to 10,000 you can tell if it is even or odd simply by looking at the last digit: for example, 7,206 ends with 6 so it is even; 7,205 ends with 5 so it is odd.

To practise, make sequences by writing successors and predecessors: start at 4,995 and list next five successors (4,996; 4,997; 4,998; 4,999; 5,000). Similarly find predecessors of round numbers like 5,000 (which is 4,999). Also mark even numbers in one colour and odd numbers in another to see patterns. These ideas are useful for counting, arranging objects, and solving simple number puzzles.

A number line is a straight line with numbers placed at equal intervals. For numbers up to 10,000 we usually draw a small section of the line at a time, for example 0 to 100 or 2,990 to 3,010. This helps to show position, order, distance between numbers and addition or subtraction by jumps.

When plotting a number on the line, mark equal spaces and label the points with numbers. To show counting forward, make rightward jumps; to show counting backward, make leftward jumps. Use the number line to find difference by counting how many jumps separate two numbers. For larger jumps use hundreds or tens as one step (for example each mark could be 10 or 100) to keep the line clear.

Number lines also make rounding easier: see which marked point a number is closer to. Practise drawing neat straight lines, marking equal spaces and labelling correctly. This visual tool strengthens number sense and helps with many arithmetic ideas.

Rounding makes a number simpler by replacing it with a nearby number that is easier to work with. To round to the nearest ten, look at the units digit. If the units digit is 0–4, round down (keep the tens digit same and make units 0). If the units digit is 5–9, round up (add one to the tens digit and make units 0). Example: 3,742 rounded to nearest ten → 3,740; 3,745 → 3,750.

To round to the nearest hundred, look at the tens digit. If tens are 0–4, round down to the lower hundred. If tens are 5–9, round up to the next hundred. Example: 6,234 rounded to nearest hundred → 6,200; 6,250 → 6,300.

Rounding is useful for estimating answers and checking calculations. Practice both methods and write rules in short form to remember. For numbers that are exactly halfway (e.g., 450 when rounding to hundreds), standard rule is to round up to 500 at this level.

When we add or subtract numbers up to 10,000 it helps to line up digits by place value: units under units, tens under tens, hundreds under hundreds, thousands under thousands. First add or subtract the units, then tens, then hundreds and thousands. If a column gives a number 10 or more when adding, carry over to the next column. If subtracting and the top digit is smaller, borrow from the next left column.

For example, to add 3,478 + 1,729, add units 8 + 9 = 17 (write 7 carry 1), tens 7 + 2 + 1(carry) = 10 (write 0 carry 1), hundreds 4 + 7 + 1 = 12 (write 2 carry 1), thousands 3 + 1 + 1 = 5 → 5,207. For subtraction 5,002 − 1,478 borrow where needed starting from tens or hundreds. Using place value keeps work neat and reduces mistakes.

Practice with different examples, including zeros, helps to be confident with carrying and borrowing across several columns.